The thing is, it's not practical. One thing is when you are disallowing on "forward only" movement. Different is, when you need to disallow on games that have to keep separate data between each other AND need to be able to transfer to each other.Strictly speaking all they'd need to do is disallow PLA moves from going into SWSH (something Bank already did with ORAS in gen 6 & USUM in gen 7)
This is expecially problematic for TR / egg moves that may not be in a given game: what do you do with a pokemon that knows a egg move in BDSP that doesn't exist in SwSh/SV? Do you constantly force the player to delete moves (potentially, non relearnable ones like limited TMs in BDSP or legacy moves if carrying from older games) every time they want to move a pokemon to Home?
Sure you "can" but it's extremely annoying.
The separate moveset was the obvious choice. I'm still on the assumption that SV will "keep" the SwSh data and BDSP/LA will just be their own exceptional thing, but I mean, that's just speculation as we know, and with the "update rate" of Home, I doubt we'll be seeing compatibility with SV until at very least early 2023.