With team attack off there are potentially way to many infinites and abusable strategies.
For instance, one person can grab an opponent and the other can do a rapid A combo to keep them locked in infinitely, or one player can grab/do any attack that keeps the enemy immobile like rapid A combos/Pit’s >B/MK tornado, and the partner can do something like Falcon punch or another big damage, big radius move like Warlock punch, Snake Fsmash, PK fire, Lucas Usmash, etc. without any risk to their partner. Grab > partner attack combos can still be done with team attack on, but spacing is much tigher so as you don’t hurt your partner, and you can’t hit with big radius moves like explosions and whatnot.
Also, projectiles become too good with team attack off, since you can shoot thru your opponent. If you have two characters with good projectiles, on a team like Pit/Falco, they can just camp at one edge of the stage and spam projectiles and make it near impossible to approach. Also, you can projectile through your partner and make their approach impossible to defend against. Using the same Pit/Falco team Falco could SH blaster through Pit as Pit does his >B, making it impossible to go above or roll through Pit’s attack.
Basically, with team attack off there isn’t much defensive strategy, it’s just spamming whatever high priority/damage moves you can and hoping you do more damage quicker than the other team. Moves that are laggy and punishable normally can become 100% safe with your teammate attacking through your hitbox.
With team attack on it also allows you to work more closely with your partner. For example, Lucas/Ness can use their teammate’s projectiles to heal themsevles with PSI magnet. You can also save your opponent from not making it back to the stage if their upB falls short by hitting them with a weak attack such as a projectile to give them their UpB back. You have to be more careful so as not to hit your opponent, but it adds more layers of strategy. If you’re just throwing out random attacks hoping they’ll hit, it’s a lot less skilled.
Also, Ganondorf moves up quite a bit in teams.