"game development universities" are a grift. You can learn what you need to online, for free.
Especially if you're an American, and not personally wealthy enough to be able to float the debt for a degree that no one will care about, going to school to learn any kind of software development would be idiotic.
That said, it would probably be best to focus on the most popular game engines just because that experience is more valuable and the community around them more developed, but encouraging vendor lock-in only leads to the normalization of exploitative practices. People should experiment and try new frameworks when they can.
A lot of the people who switched to Godot after Unity's license debacle remained. A lot left for Unity as soon as they started acting reasonable again, and they had a lot of complaints about Godot which have only made the framework better, and more competitive, and Godot will be more attractive to them the next time Unity screws them over, which it now knows it can do. That can only happen if developers take a risk on investing in alternatives.