The Euros have €250 and €500 bills that are very useful. Both were available in ATMs last time I was in Italy. Why can’t America have some larger bills like that?

I'd say I'm all for that. The larger bills would be excellent for general use. Much much much less bulky to carry around, versus fistfuls of smaller bills.
Only thing is, the virtual certainty that any ATMs containing any large-denomination bills would be immediately stolen by "certain elements" (who have a decades-long history of doing exactly that type of thing).
The illegal drug trade.