For one, it's not an option for everyone, particularly the less able bodied. But more importantly, being the weak link in sports team can actually be a very isolating and lonely experience. Even if it's a casual/intramural setting, if you suck at the sport and are actively causing your team to lose, you will more than likely not have a good time and will not feel more connected to people, even if they make a good faith effort to make you feel welcome and included despite you being a detriment to the team.
Source: I joined a casual sports team to be less lonely, and ended up feeling socially worse off for it. Not saying that will be everyones experience, but I would "totally vehemently disagree" that it's an unequivocally better option than volunteering.