Not really
And I agree with the OP, it's a bad model to use. The media corporations love it, it sucks for the rest of us.
There is no team sport I know of where an individual can voluntarily switch sides, where they can support one team on one issue and the other team on a different issue, where you can win by making a good case for the things your party believes in and people from the other side join your side.
Some of the right-wing is beyond hope, we will never reach them. Many of them, however, are low information voters who have been duped into working against their best interests. Some of them can be won over, rather than crushed and defeated.
To what degree? I don't know, but it's the right approach, we're governing a country where winning doesn't mean defeating the other side, it means governing in the interests of the people.
So, there are ways to govern in which members of both parties benefit. I don't mean implementing part of what the Republican party wants, I mean putting policies in place that help the people, all of them. That's winning. Clearly different from team sports.
Unfortunately what we've been seeing is governance where the financial sponsors of both parties benefit, and we're all paying the price for that. Who wins? The owners, while the players all lose. So again, clearly not team sports.