If your team always wins, there is no point in supporting it, no thrill. Everything in moderation, even winnings.

Is it really symmetric?

I imagine generally the upper limit on always winning is higher. As in, usually the person consistently losing wants to stop playing before the player consistently winning.

Also if you have time to play multiple rounds, then with a handicap you can set that you both have 50-50% chance to win, thus making the game really good, with adrenaline, the possibility to do your best for an extended period of time, and the reward for that.