It's an interesting idea. And you're right, that if the SEC and ACC are able to play this fall, I wouldn't think they'd be interested in delaying the start of the fall 2021 season just so the Big 10 and PAC 12 can safely play after a spring season.
But, with Christmas break, I'm not sure how early into 2021 spring football games could even start. Then there's the issue of fans. As to your question about indoor facilities, I would be surprised if any Big 10 team didn't have that available, but I doubt many (if any) would have space for fans beyond immediate family members of the players..