You can work as a web dev at a small company without being part of the mainstream silicon valley rat race. Sysadmin-type skills are pretty hard to hire for, and very useful at small companies. It sounds like you've got that going for you. I'd change your definition of success and focus on finding a job at a company with a culture you'd enjoy, and not worry so much about its perceived prestige.
The reason why accounting, banking, consulting need their Big Four / Big Three is because it's hard to measure what their people actually do, so they rely on joining a big firm to reflect their worth.
In software engineering, you should be able to describe to someone in tangible terms what you've worked on in the past 3-6 months and what value it's brought to the company (and if you can't, start writing that down because you should always be ready to discuss that with recruiters or your boss when you want a raise). Because of that, we don't need the prestige of a namebrand company when we jump to the next job.
You should ask yourself why you'd want to join a Big 4 and if it's actually necessary. If it's for potential entrepreneurial connections, I can assure you that there are plenty of startup founders that are doing fine without the Google name. If it's for technical challenges, all companies have their own issues. You may not be working at Google scale, but trust me even with 5000 customers, there are still scaling problems that need to be solved for that particular case. And if you just want to work with smart people, they're everywhere. The company I work at was bought an East Coast company (outside SV!) and their engineering team are doing infrastructure things heaps better than we were.
This is an extremely humbling field and regardless of where you work, there's always something to be learned.
It's kind of funny that a position at one of those companies is now the new mark of prestige instead of a college degree or something. Shows how far the university has fallen.
Does it? Unless things have changed, graduates of elite universities are disproportionately represented at the AppAmaGooBookSoft companies. It seems more accurate to say that those companies play a similar role to HBS and Yale Law.
Is it Valve?
Even back before Google existed, having MS on your resume would open doors at software companies.
Google has always been a gold star.
But it isn't instead of universities, it is as well as. Stanford/MIT/etc will have the same effect.
Maybe it shows how little I know, but I think Valve and other companies who do this are doing themselves a disservice by basically using Google's recruiting department as a passthrough (and, as an autodidact programmer, I feel essentially the same about people who put it all on educational pedigree -- this isn't an endorsement of the baseline credential, just an acknowledgement that what constitutes it is shifting). It feels like an admission that they don't know how to hire, so they're effectively offloading that responsibility onto companies whom they believe have thorough vetting processes.
Also the Big 4 are changing every few years. Is Twitter still considered part of that group?
It's clearly currently five. In order of market cap: Apple, Alphabet, Microsoft, Facebook, Amazon. Note that these are now the five biggest publicly traded companies in the world, not merely in "tech" (a clearly archaic categorization).
This isn't exactly a strong line though, since all are at least diversified into things outside software.
Nevertheless, that was the original reasoning.
Your points are valid, but they're not the complete picture. Otherwise we'd all be clamoring for jobs at Googlezonsoft, but as sentiment shows in this thread; that's not the case.
My main point was to emphasize that it's possible to find job satisfaction outside of the big companies and that one has to question and determine if a big company would be a good fit, or is it purely an ego thing.
The main point point I tried to get across (somewhat unsuccessfully) is that I need to work in an environment with a passionate, hard-working, highly-capable team in order to justify the time I have spent (and will spend) on software engineering.
The main impediment I've found in turning this goal into a reality is the technical interview. The way I see it, I either improve and make it happen, or I don't and move onto something else.
I would highly recommend you read the book: Decode and Conquer. I would also recommend Cracking the Coding Interview and Cracking the PM Interview. If you can solve those problems on a white board, you can pass a technical SE interview.
I would also suggest you:
1. Work on a problem for a few minutes and try to solve it. If you can't, look at the solution and understand how the solution was derived. Go back and solve the problem again. You are not finished here. Go back a few days later and work on the same problem - repeating this several times a week. Over time, you will grow more confident and can quickly recall concepts that are potentially causing you to perform poorly on your technical interviews.
The one thing I wish had been made clear to me beforehand was understanding just how little the non-tech and business savy people knew about what we do. As such, despite how much of a positive impact I had, my pay was not even close to what it should have been (first-year photographers were making more than me). It was a constant battle to explain why certain time was needed to complete various tasks, as well as why I was putting in the hours I had.
When I finally managed to get out of there, feeling underappreciated, it was THEN my once boss realized how lucky he had been. Nobody would come and work for the same pay while being asked to do all that I had done.
So be careful and at the very least prepare yourself if trying to go into smaller companies and businesses.