Let’s reverse the situation, they were able to add ads to sport events, so they can definitely remove ads and show the main event cameras if they wanted to. But they’re picking up showing ads indirectly through some other service.

Who is "they" in this situation?

I noted that the streaming service, like Paramount+, would be able to overlay their own ads over the broadcasted commercials, but they won't have control over the cameras. That's on the broadcast station, they're the ones controlling the remote production.

Paramount+ can only rebroadcast what my local CBS affiliate is broadcasting.

I think only Netflix and Prime have deals to actually produce sports broadcasts.