Tbh I never really saw the identity of Cloud's father as some loose end or grand mystery. I mean, I suppose the theory is possible (if you don't take Cloud saying his father died when Cloud was young at face value), but from a narrative standpoint I don't really think a familial connection to Shinra would really add that much since Cloud's rivalry with Sephiroth overshadows the conflict with Shinra. It would also kind of make the world feel sort of small, IMO, to have Cloud's dad be an already established character.
I fully expect the remake to use it as a big reveal and link in to Cloud being some sort of chosen one.
I wouldn't put it past them, but I really hope the remake does not do this. Cloud not really being anyone special (by JRPG standards) is what makes him an endearing character, IMO, and how the original game handled his past is quite clever - there's more to it than meets the eye, but, unlike in other games (FF and otherwise), the twist
isn't that he's a super important person. In some ways Aerith is more the typical chosen one type character, and the game toys with expectations regarding her, as well. I'm hoping that the remake doesn't attempt some misguided worldbuilding that results in it falling into the more played out tropes that the original seemed to deliberately avoid.