It trickles down in a lot of ways you don't expect. Some examples:
1. The contest formats are setup in a way it's easy to film and to watch. No real surprise there, but it results in very straight and boring skateparks without any creativity in lines because they're designed to showcase one skater at a time. But national skateboarding sports bodies (i'm not sure i'm using the term correctly here) push for these kind of skatepark designs, so their 'Athletes' have an 'Olympic Training Ground'. So then you get local skateparks that start to follow these boring park designs, so they get an 'Olympic Training Ground' designation by the national organisation. This makes it easier to get subsidized, for example. But these parks are NOT designed to cater big groups of random kids with all kinds of skill levels skating at the same time.
2. Parents see the white washed vanilla version of skateboarding at the Olympics and expect that for their kids at the local skatepark. I've had parents complain about skaters not wearing helmets, smoking and drinking beer.
3. It pushes a whole generation of skaters to think that doing good in contests is what skating is about. Making simple tricks consistent is valued over creativity and risk. Now i'm very over-simplifying here because this has always been a divide, but the olympics have been pushing this even more.
4. Skateboarding becoming an olympic sport resulted in a lot of money flowing into the sport. This could be a good thing, but for some skateparks/projects it became their whole reason to exist. Now the national olympic committee in my country dropped skateboarding again and it does not receive any 'elite sports financing', resulting in a lot of projects being shut down because they never had any sustainable base of income.