I've been on both sides of the fence before and I know what a grueling process hiring is for both applicants and managers, so I certainly appreciate the time commitment that goes into hiring. That said, if your company wishes to present itself in a way that is caring of its employees, a great first impression would be in the hiring process.
One of the best interviews I had was very informal, was only with the hiring manager, and it was pretty obvious that there would be a good fit between myself and the company. I took the job and had no regrets over it.
One of the worst interview processes I went through had me doing two rounds of phone interviews and then a half-day in-person consisting of four one-hour interviews with various people. The selection of people conducting the one-hour interviews were fair enough -- HR, hiring manager, a peer, and someone from a related department I'd have contact with but wouldn't work with frequently. But you could easily tell there was no organization behind what they were doing, unless their strategy was to have each of the persons doing the interview have the same exact conversations with me. This was at a Fortune 500 company and it became clear from the interview process that the culture would be extremely frustrating for me to work in.
I think it's fair to follow a process like this to respect the time of your applications:
resume cover -> screen -> phone interview -> in-person interview -> tests/samples -> hire
And you drop people out of the funnel at every step. I also think it's best to keep your in-person interviews to two hours max, between however many people they need to talk to.
Technical tests are a double-edged sword. For candidates with little to no prior work experience (fresh out of uni for example), it makes sense. Unless serious question marks arose during the prior interviews, I find it disrespectful to play the "stump the candidate" game with candidates who come in with 10, 20+ years of experience. I'm not aware of any other industry that deploys a barrage of obscure technical tests on their candidates the way some companies do in IT.
Although trick questions and the like are bad, and a sign that you should avoid the company giving those questions in an interview.
It's not like they threw a black bag over your head and tossed you in the back of a limo while you walked down the street...
I haven't showed up on-site for an interview without discussing the role and discussing money (in numeric terms, not vague ones) since I was 24. It's more common than not that our ranges don't overlap, and I find that out on the phone with minimal investment and inconvenience, not in-person after expending a lot of time and effort. (It helps both sides to discover that early.)
'Attempting to “solve” these problems means that as a
company you have to throw away everything that you know
and start from scratch.'
These rough edges aside, the structure seemed incomplete. After his unfiltered stream of problems and process, he then says ~"throw away everything and start from scratch" and throws in a quote from a self-improvement, business book, as if he just did everyone a favor.
A process that admits some variability, even if by accident, may make your organization more robust in the long run by avoiding mono-cultures, both technical and personal. Some of the skill areas that my employer depends on, including mine, were hired by accident.
The most frustrating thing is HR won't let you see what's out there and adapt your requirements to what's available.
P.S. Though personality tests are EZ to juice, as you mention, they're still a low-pass candidate filter. Honestly, I see their biggest value as "just another ploy" to wear down candidates during interviews.
This is because in practice, "culture fit" is the current buzzword excuse for what is otherwise called "illegal discrimination".
The problem arises because the culture is largely a factor of protected classes. It is acceptable to not hire a woman because she is a worse candidate than a man who is also applying. It is unacceptable to not hire a woman because she is a woman.
But when you account for culture fit, she may end up being a worse candidate because she is a woman who would be working a culture that is toxic to women. And often, getting rid of those who make the culture toxic to women isn't an option in the near future.
The term can mean a legitimate work compatibility issue like "people feel awkward around him when they try to crack innocent jokes to ease the stress", but can also mean "he insists on picking up his kid every day rather than going out drinking".
But how do you filter that out? You need to know exactly what you're looking for.
But as soon as your "cultural fit" becomes about hiring young, hip dudes who like unusual food and kite surfing, it becomes a harmful aspect of your hiring process. You'll end up with less diversity, and therefore less represented view points in your company, and therefore less customers that you will understand. Diversity is important.
Seriously, look at the report from Google just for a much-discussed recent example. It's not like this hasn't been discussed at length on HN.
The former is clearly ripe for abuse, the latter is more legitimate (though also a place to tread carefully).
Of course, you need to give the person a chance to ramp up, etc, but if they can't be a contributing team member in 2 months, then it's better to give them 1-2 month's severance and get rid of them. I know one late-stage startup in the city that is using this technique, and I believe Netflix uses this technique as well. It sucks, and kind of creates a bit of a harsh environment, but it's a fast way to build out your team, and probably has the same success rate as any other interview method, if not better because you cull your bad performers quickly.
Um, what does that mean in practice? "do your best" is pretty much meaningless. "Someone who seems smart" seems to invite hiring by stereotypes.
An HR department is not a "big company" thing that's there to get in your way. Its job is to do things like (e.g.) protect the company against liability in messy sexual harassment scenarios or (e.g.) hiring discrimination lawsuits.
The substitute for this functionality is not goodwill or "just doing the right thing" because this role necessarily involves a detailed understanding of employment law. If you disregard this department when building your company past, say, tens of employees, you are basically certain to be in for a bad time later. The book is written here by companies like GitHub, who have had major scandals that could have been prevented mostly or wholly by a competent HR department. If you look at their example and don't learn, then you are a fool.
Beyond filing paperwork, I agree that hiring shouldn't be an HR job. Unless HR is hiring for HR, let the teams decide who to hire.
Often they hire based on just that. If they don't, step two is usually some sort of assessment, and the assessments I've done tend to be pretty good.
It is possible that I've forgotten a ton of interviews with crappy companies that I didn't end up working for. The interviews I remember are the ones that worked.
Lots of people are looking to catch a break, score their dream job, or just see what's out there, while many more just need something to pay the bills. In almost every case, applicants can't win what they don't put in the middle -- which means that they have to apply if they meet even some of the position requirements.
Unfortunately, for every well-qualified applicant there are many less-qualified applicants, and the deluge of applicants means that it's simply not possible to review each person individually. Instead they get run through a filter built from loose heuristics that try to capture job requirements.
I've long felt that the solution here is the same as a busy nightclub: charge a cover. For someplace like Google that gets hundreds of thousands of resumes, that'll cut down on the applicant pool quickly. Reimburse it with a bonus for candidates who make it to the interview stage. It's not about penalizing applicants, it's about encouraging applicants to be honest about the fit between their skills and the position requirements. I predict there would certainly be fewer applicants failing FizzBuzz.
Employers are also hypersensitive to false positives (candidates who don't work out), and a (justified) fear that they'll invest in a candidate who will move on after learning and maturing in the company. It sucks having to fire someone who isn't working out, and it can hurt morale even if the employee wasn't producing. The cost of onboarding, training, and firing a candidate sets a high threshold against false positives. It's just as bad when a new employee is working out well but leaves abruptly for a better offer. I don't have a solution to the former, but the latter is usually a good indication that you need to review your compensation policies and the overall competitive positioning of your total package compared to the market. Happy employees don't usually leave; people quit when they don't have advancement potential, when they don't feel fairly compensated, and when they're bored. 
This wouldn't work for me. I rarely know much about the company I'm talking to. Once I was so amazingly off the mark about what the company did (I must have confused them with another, though I still don't know which one), that _I_ was shocked and disappointed with myself. I still got the offer. (I turned it down; I would have been good at it, but I got something closer to home instead.)