I don't think apps have to be FOSS. It's super important for libraries, frameworks and other infrastrucuture related stuff to be FOSS, but you can always change a client.
I totally agree! I would much rather use lemmy with a proprietary client than reddit with a FOSS client. But when I have the choice to install something from f-droid instead of aurora store, its an easy choice. Also, wefwef works perfectly for me, so why install anything at all xD
I use sync, but I think they still should be FOSS, or at least open source. Just because when anything gets left behind or never fixed, you can take it and patch it up yourself. That includes clients too, lots of good clients that get left behind because Dev stopped and whatever they were interfacing with changed.