I don’t think so, F-Droid should not be viewed as a play store replacement for the masses. I would instead consider it an opinionated store / repository for apps that have to fulfil some pretty strict criteria. This makes it a great resource, and a good complementary resource, because that allows them to be picky and stick to their values. And it enables people that don’t mind the trade-offs to restrict themselves to F-Droid without having to research every app themselves, if they want to.
Most general users would hate the idea of dealing with multiple app stores, but I think some fragmentation like this would have some benefits as well. Note, for example, that F-Droid does not focus on quality of apps: There are lots of little projects that maybe don’t look super polished or are in early development, etc., and that is great. But there could just as well be another App Store focusing exclusively on high quality, feature-rich apps, while taking a more lenient stance on open source code and it being free. Or whatever kind of focus you want to place.
Then again, this could be achieved with a good search function and filters as well. In the end, what F-Droid offers is more choice a better place for apps that Google decided to ban from their play store for strategic reasons.
I would avoid it, if you care at all about availability and downtime. The result will probably not be great, you need to ensure the server side gets enough resources under load, and setting it up may require constant restarts if things aren’t immediately working as expected.
Nonetheless, here is a link where someone did essentially exactly that on NixOS: https://astrid.tech/2022/09/22/0/nixos-gpu-vfio/