Because notes (bills) are routinely scrutinised for forgeries, and there are lots of security features (watermarks, metal threads, UV inks etc) that are very hard to forge in such a way that they pass scrutiny.
Coins, on the other hand, are effectively just a hunk of metal, and more importantly, nobody pays much attention to them because they’re not worth much. You get a handful of change, you’re not going to look at it closely as you would with notes.
So once you’ve got your mould it’s much easier to produce a few tens of thousands of fake coins and pass them than it would be to make banknotes, even though the value may be less.
£1 coins tend to be targeted because they are the highest-value coin that is easily faked. We have £2 coins as well but they are bimetallic, with a gold-coloured outer and a silver-coloured inner (pic), so would be much harder to fake.
Also remember that a pound is worth a couple of dollars; with one or two of those I assume you can still easily pay for any of numerous small items, so it would be easier to pass one off on someone. Presumably it might be less easy to go back to that establishment a second time.
U.S. circulating coins are worth so little that we virtually never use them, without bills, to buy anything of significance, and hence the only place anyone could really try to pass off a bad one would be a vending machine. Any illicit gain from passing a bad quarter off on a human shopkeeper would not be worth the trouble.
