I’m sure plenty of fighters would disagree that there’s no team element in fighting. Every time one of our muay thai guys would fight they’d come back and say they couldn’t have done it without the team, they always credited the team/gym as being an integral part in their development, especially their training of course. Sparring partners are team members, sure they don’t fight with you but does that necessarily mean you’re entirely on your own?
I’m playing devil’s advocate here, as I’ve no real preference between one on one sports and team sports. I love both and have done both. In my personal experience though fighting (muay thai specifically) was WAY more challenging than the team sport I did (soccer) and I was arguably better at soccer than I was at muaythai (judging by how often I got my ass spanked)
If we could outline some characteristics then we could start edging some sports out but I don’t know if we can agree in the end. Clearly our preferences are different and you won’t ever give fighting it’s due, so no point really.