F-Droid is a teeny store and requires extra steps like open sourcing such that it is not an appealing vector for malware authors.

Either you want to target the Play store so that you can get a wider install base but need to deal with tighter controls or you want to distribute flagrantly malicious stuff to people for banking trojans or whatever via social engineering to get them to sideload. F-Droid doesn't help with either of these things.