Besides big ones like soccer that you mention, more niche sports are often partially or totally outside of school systems.

Fencing for example, is usually clustered around external clubs. Very few high schools will have fencing teams, and in a lot of cities even the high schools that do have fencing teams will be kind of a joke compared to the club teams.

This comment made me curious so I did some research. Of the sports offered by my local school district (in the top 30 for enrollment in the country), I can find an alternative for homeschoolers that offer competitive opportunities for every sport but bowling and football.

Of the others, there are either homeschool alternatives that are explicitly secular or at least not overtly religious, or there are competitive clubs. All the schools have track & field, but there is a large homeschool league. And the district has a few schools with pools and a few more with swim teams that practice at the city pools, but the local swim club is the one turning out the Olympians – but even then, it also seems to have plenty of offerings for kids who won't set a world butterfly record. Football, I imagine, is just so popular that the private/public schools take all the players.