Many journals allow this; less commonly funding agencies. But most of my collaborators are not programmers and do not know LaTeX, and for a non-programmer it is very difficult to learn.

Besides, I don't love LaTeX. It is a very heavyweight markup and seemingly takes forever to get things "just right".

That depends on the field (and publication), maybe it is less typical in biology? And all the research funding instruments I've used require (or at least very strongly hint) you to use Word for submitting applications.

If LibreOffice docx export does not work correctly (or import missed crucial fields / paragraphs) with the funder's templates, you might get rejected. Academic funding is already so fickle that I wouldn't even try. (Personally, that's always a major hassle, as I have to find a computer with correct version of Word installed and borrow that for some time.)