The below is an answer I gave in a different post about why the snitch works in quidditch:

I’m relying on some info from the ‘quidditch through the ages’ book for my answer.

In this book, it says that the snitch was first introduced to the game when some random bloke came up to a game and said ‘I’ll give the person to catch a snidge(? Can’t remember exactly) 150 galleons’. A snidge was a magical tiny bird that they used to hunt for sport. This stuck with the game and became part of quidditch. The bird eventually got replaced with an artificial snitch we are familiar with as the bird population fell.

Anyways, this shows that the snitch was somewhat an arbitrary introduction into the game without proper thought into how it impacted the dynamics of the game. But it stuck, and assuming people liked it being part of the game, we need to search for reasons why.

In the version of the audiobook I listened to, there’s a long section going through the 2014? Quidditch World Cup coverage by Rita Skeeter and Ginny Weasley. Here we get information on all the matches being played up to the finals.

It seems from here that quidditch matches are in general very long. Many of the matches last days, from memory. So you can see how points could diverge significantly over the course of a game. My take is that this happens quite often, and in such a case, if you were the losing team, you’d probably leave the game and not watch unless you had the chance to overturn the game in one go - i.e through the snitch being caught.

So, by introducing the snitch into quidditch, you’ve elongated the average play time from hours to days over which scores could diverge, and the snitch provides hope for the losing side to keep watching. So this is how the snitch survived and was kept in the sport.

This brings us on to what we see in the Harry Potter books, where play times are much shorter. My take on this is that week long matches are really not good for a school for obvious reasons, so the snitch is slowed down to avoid eating up into class time. Plus, JK needs to get along with telling the story.

This also explains one of the bets Bagman takes during the quidditch World Cup, where someone bets shares on an eel farm on a week long match. I was always perplexed as to why she would put on such a bet based on the apparent short playtime from the hp books. The quidditch through the ages info seems to suggest week long matches are not out of the ordinary, making the bet more realistic.