Ignoring the coin jar/charity box confusion, I've tended to keep the bigger coins around and just spend them - a few £1-2 coins don't weigh that much, aren't taking up a great deal of room and will buy your lunch entirely. Then they're not your problem any more.

500 yen's over £3, so I'm guessing you don't get many of those in your lunch change? The top result for "how much is lunch in Japan" [1] suggests that your 500 yen coin would just about cover the next day's lunch and is lighter (barely; 7 grams versus 8.75g) than a British one pound coin [2,3].

The coin sorting machines that you might tip a coin jar into take a decent chunk of your money for the privilege of counting it (e.g. CoinStar charge 9.9% [4]).

1: https://www.withhusbandintow.com/costs-to-eat-in-japan/

2: https://en.wikipedia.org/wiki/One_pound_(British_coin)

3: https://en.wikipedia.org/wiki/500_yen_coin

4: http://www.coinstar.co.uk/FAQ

Who said anything about charity?

Ah, I think I misread the original comment to be something like "drop the coins in the tip jar". Please disregard.

OP is dumping the change at home, then converting it to bills all at once.

That works even when coins have non-trivial value.