A good way to pick battles is not to fight most of them. There are so many solutions that don't have any real problems...

Could you provide an example of solutions without real problems, game engines or otherwise?

Basically anything overengineered? Concrete example: C++ "manager" objects. Why not finally learn how to structure applications and keep allocations and resource use in check? The program will be so much simpler, compile quickly, be easy to understand (execution threads stop jumping around like crazy), and typically have less memory leaks / use-after-free etc.

RAII, garbage collectors and other fancy inventions for freeing resources from the call stack automatically? Not needed. Use global resource managers. Globals are needed and semantically the right thing. Not a problem.

Any crazy programming language with all the features they could conceive? The one you need is guaranteed to be missing. Better, express your problem yourself and write a simple generator script that translates your concepts (mostly as plain old data) to the minimal language.

Another: XML (and even JSON), possibly for anything except true document markup. It's slow and doesn't buy us anything. Yes, there are ready-to-use parsers, but after parsing you still hold a mess in your hands (and only strings / floats). Finally learn database basics and manage data in tuples. Make a text file parser that takes simple table (= list of column types) descriptions and then parses tuples from single lines and puts them as typed data in arrays of structs, done!

How does a "global resource manager" work and in what way is it better than RAII and garbage collectors? Googling wasn't helpful.

Just global state. Simple example, a global variable that holds an allocated memory buffer. You initialize it at program startup and tear it down at the end (you can be sloppy and leave out the latter). While the program is running, you re-allocate as needed.

This is better in that it really is a very simple thing to do. There are no possible memory leaks. But what happens is much more explicit - you have precise control, and no bumpy control flow (much nicer for debugging).

But it doesn't have to be memory. If you want to look at my project https://github.com/jstimpfle/learn-opengl (careful - it's not tidied up. But I think it demonstrates my point), most resource state there is global module-wide state. I simply have init_module() and exit_module() pairs that I call from the main function. Problem solved. Not a headache at all.