Yes, that is the problem, precisely. Lualatex and xelatex do not support all the features of plain latex (mostly "hacky" things, like pdf controls, js animations in beamer, etc). So, you have to chose between using these features and being able to type unicode letters directly.

Probably there is a magic combination of engines and packages that allows to do everything at the same time, but I haven't found it.

If this works natively in typst, it's a great selling point for me (although I dislike the markdown-like syntax).

Uh, pdftex, xetex and luatex should support everything of the original tex engine, but each has extended tex, so some things will work on pdftex (which I think is what you're thinking of as plain latex), others on xetex and then others on luatex (or pairs of engines, I know microtype works on pdftex and luatex, but not xetex). I don't think this is an tex specific problem, more a natural result when there's multiple implementations.

I suspect as typst only has a single implementation (I believe), it won't have the problem of different engines ;)