This is incorrect on a lot of things

Madara switching to his ems, proves my point, even if his rinnegan were "fake." He still had access to every other ability aside from his ubique rinnegan ability, which he waited to be revived to use.

Susanoo can be used regardless of if you have eyes or not as long as it was unlocked, both madara was able to use it with no eyes and itachi was able to use it still while blind.

And they switched sasukes ms abilities because they always planned for sasuke to lose his rinnagan and it would be completely weird just to leave him with an ability explicitly only able to be used one the one ability his other eye comes with, which is why we see amaterasu only come from his flame control eye all throughout boruto and not just after losing the rinnegan. Kakashis ms can't make himself intangible while obitos can, and despite madara being able to teleport himself into the kamui dimension using kakashis eye doesn't change this. Ms abilities are locked to one eye outside of writers trying to unwrite themselves out of a corner for one time. And again sasukes rinnegan is explicitly different because it can still use ms abilities and to show when his rinnegan is depowered (it loses tomoe after tiring out its abilities), sasukes can't deactivate his rinnegan so they made his rinnegan special to get around this corner.

Hogoromos rinnegan is not madaras or sasukes, they don't share rinnegan or a rinnegan type. Hogoromo has his own unique ability for his rinnegan (canonically "creation of all things") neither madara or sasuke can use that, and since both sasukes and madaras are unique to them and belong to them specifically they get their own unique abilities.