I'm not sure why anyone prefers a pocketfull of heavy coins to a few bills in a wallet.

Bills have serial numbers, coins don’t.

But the Canadian would have preferred half as many $2 coins.

There is a $2 bill, except people think it's rare and take it out of circulation, then making it actually rare and causing headaches for the US Treasury.

It sounds like the Japanese 2000 yen note (although that's worth about $20). I was given lots of them when I changed money before a trip to Japan, but had some trouble using them because no one seemed to believe it was real money. A bus driver actually had to ring through to someone to verify it.

Reading the wikipedia article about them it seems I might have been better off selling them on ebay :-) https://en.wikipedia.org/wiki/2000_yen_note

Similarish issue with 500 EUR notes. Foreigners sometimes get stiffed with them overseas because nobody wants to take them, including the money changers' suppliers. In Europe, you can only convert them at central banks, but usually they'll be accepted if you buy something big enough.

That's more like the US $100, which is not accepted usually because

- they are a high denomination bill and people who attempt to counterfeit money like to copy those

- they are not encountered often, and so staff can be unfamiliar with how to verify their authenticity

- as the highest denomination US note, it is very hard to get it out of your till and back as change, and meanwhile it has probably taken a bunch of bills you do often need to give back out of the till

Your bank will take it at least. Not so with a 500 EUR note even in Europe.

If the bank doesn't take it, how do 500EUR notes even wind up in circulation then?

Because they are more reliable and easier to clean. Machines rarely reject coins, they often reject legitimate bills. At least the ones I have used in Germany and Mexico.