I agree with you about the way that the entertainment unions work. They have their quirks, but they are generally excellent.
Just to offer some nuance, "union members are not allowed to work on non-union projects" is not strictly true. Union members can apply for waivers to work on non-union shows, and smaller theatres operate under letters of agreement with SAG-AFTRA which require only X-number of union contracts per show or per season. Also, union members - no matter their usual wage level - are free to sign contracts to work for "scale" (minimum wage for union members) on projects about which they're passionate; this happens all the time.
Incidentally, the "minimum wage" scale is also different for theatres of different sizes and business models. It's an attempt to balance workers' rights with the exigencies and economics of a fundamentally unstable industry. Some shows won't (necessarily - there are always surprises!) be commercial enough to be produced at certain theatres, and some actors may be prevented from working on some projects, but the system itself won't ever prevent anything from being done at all.
Another advantage to keep in mind if you consider importing this model to another sector: operating under a LOA provides a huge measure of protection to non-union employees, as well. At a certain point in my theatre career I stopped wanting to work on any non-affiliated project - unlimited rehearsal hours with no required notice period were unappealing, for instance, and (even as a non-union actor) pay was usually better in affiliated companies. There was a line to walk, though: once you accumulate a certain number of affiliated weeks in a rolling period you'll be required to join the union, which can limit employability: it's important to make sure your career / skills / network are sufficiently developed to support that level-up.
Anyway, I think that general model would be a good fit for tech workers, and I'd like to see it tried.