Shizuku's license disallow 3rd party recompilation of the APK, fork or not. Presumably this is done to provide an option to legally takedown fake Shizuku which could contains backdoor. (The original APK is redistributable) Hence Shizuku is not on F-Droid.

F-Droid, however, allow the developer's binary to be reproduced if they have tested that the APK is reproducible when replacing the APK's signature with the original APK.

Well, for starters it is just a whole lot less work and money to distribute and maintain binaries up from the distributers' side, for the developers it comes down to a lower-barrier of entry to not have to adjust their workflow to whatever x platform may demand for building on their servers and in the end that gives the users more choices to work with. Of course, this is all in a perfect world where the chain of trust isn't broken so easily, which isn't an easy feat but given platforms like Windows thrive in spite of it, it is probably not as bad as many people may think.

All of that said, not particularly speaking for OpenAPK here, given their motives seems rather unclear to me. If I am to be charitable, I guess they're just trying to provide a different platform than f-droid for discoverability, but for whatever reason they seem to be marketing the distribution-side of things more which is just odd to me, but alas.