If you want to be evaluated in a more holistic manner (including side projects) you'll probably have better luck with very small companies. When the people in charge will actually be the ones working with you every day, and they are only filling a small number of positions, they will be more likely to find it worthwhile to get to know you as a whole person during the hiring process.
Unfortunately, once a company is beyond a certain size this just isn't possible because it doesn't scale. They have to fill hundreds or thousands of positions and also maintain a universal set of hiring standards. Things degrade into a game of numbers. This makes cookie-cutter tests almost inevitable.
While frustrating in their own right, for me what makes things worse is that you have to do one of these screens for every single company you apply to. And most companies have the same evaluation goals for the phone screen stage (e.g., do you actually understand data structures & algorithms).
What I'd really like to see is the emergence of something like a "common app" for software hiring. Outsource technical screening to a reputable third-party, and once you've proven yourself by obtaining a good enough "score" you can move immediately to on-sites (what constitutes a "good" score would vary by company). This doesn't solve the problem of the efficacy of technical screens, but it at least cuts down on all the redundant effort.
Two services I've tried so far that are doing something like this are Interviewing.io and A-List. Unfortunately it seems these services merely make it easier to get a phone screen, rather than replacing them. But it seems like a step in the right direction.