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The US seems to have entered a stasis of coinage (and bill) denomination since before I was born (a long time ago). Besides getting rid of the penny, pretty much every attempt to introduce new currency (like $1 coins) have failed. And I wouldn't count on being able to use anything bigger than a $20 bill at a random location.

And, at this point, cash use is in sufficient decline that I can't imagine any serious effort to make changes.

Canada no longer has pennies. Canadians now seem a little surprised that we still have them. Comically, US banks accept Canadian pennies so people are using them up as much as possible.

My long-held theory on this is that low denomination currency acts as a slight break on inflation.

I believe the (plausible) conspiracy theory is that the zinc industry lobbies to keep them going. Somewhat ironically, it's long cost more than one penny to make a penny. I believe 1982 was the last year they were made entirely from copper, but eventually even the cost of zinc (often known as "pot metal") outpaced the value of the penny.