I don't disagree with anything you just said, but I think the solution you're trying is potentially even more confusing. I don't have a better idea.
Yup this is confusing
Yea not sure what the best solution is, but feels important to include the ₿ somewhere. We can also show the USD equivalent amount in the UI or let you toggle to sats. We'll test it out and share feedback.
Using doggie coin instead is a better idea imo
₿ for bitcoin $ for sats, the $ symbol is ours now