> also sends gray bubbles
Incoming messages are _always_ gray on iOS, irrespective of the use of iMessage or SMS. Your solution is not any different in this regard.
I’ve never seen a gray bubble and have received incoming messages from all different types of accounts
Incorrect.
It looks like in iMessage for business, the phone’s user’s outbound messages show as dark grey (as opposed to normal iMessage and SMS/RCS which show outbound messages as blue and green respectively). I assume this is supposed to communicate that you’re talking to a different sort of entity, not a normal person on a phone.
Personally I don’t see why you’d care. My business isn’t trying to pretend to be a normal person using a phone, so why would it matter?
https://www.apple.com/ios/business-chat/