The intransitive use of 'enjoy' is now fairly extensively used by semi-literate restaurant staff in Britain too.
I agree with the OP that English greatly lacks a suitable term for enjoining your dining partners in the way that 'bon appetit' does in French.
But English, across the centuries, has overcome natural deficiencies, by simply borrowing a foreign expression. Are there really many people in America who wouldn't understand what 'bon appetit' meant? I alternate it with 'Guten appetit'. But doesn't Spanish have an equivalent which Americans might use?