I'm somewhat familiar with the tech used to display those boards, and I think the most efficient way to remove them would be to pass the image through an AI taught to scrub them out. And I understand how grossly inefficient that is.
The other option would be to get a 'clean feed' of the broadcast before the ads get overlaid- while technically this would be relatively easy, contractually it would be difficult, as the event host is paid to put ads in the broadcast. You'd essentially have to pay more than the advertisers do. This will still leave you with the 'traditional' ads, the physical signage and stuff written on the turf, etc.
You could potentially pay the stadium to have these removed, and if you bought the teams competing you could remove advertising from jerseys.
If enough people paid for a subscription, there's the possibility of an ad-free sports league. I shudder to think of the price, though.