Most coins taken from your change are unlikely to be worth more than their face value.
Most collectors prefer coins in the best condition possible.
Circulated coins usually have a considerable amount of wear. Even tiny scuffs and scratches, or fingerprints are unacceptable for many collectors. There are a few people who collect coins from circulation, just for the fun or challenge of finding different types, or a complete set of different dates. Of course, such collectors obtain their coins at face value, and they are usually reluctant to pay any extra. The earliest coins in circulation in the UK date back to 1971, hardly any time at all for a coin.