"...can be told apart by feel."

Yes, if you are paying attention and use enough of each to stay in practice.

As to the govt., if they just quit USING dollar bills, the new coins would BE used...and if they made lots of $2 bills, one would never need to have more than ONE metal dollar at a time, if they chose.
Dollar coins could go in registers in the space where 50¢ pieces used to, and $2 bills where the ones were. It would save millions each year.