I think Yoshi is actually pretty not-okay in teams.
However, if you play with a teammate that is truly a teams player, you will notice that Yoshi is actually good at saving and can be saved, but by a medicore group of characters and not everyone.
Grabbing is bad in teams, so I don't necessarily think that plays to Yoshi's disadvantage.
The big part is that he's easy to hit and his defensive game is slow, which is something that is easier to overcome in singles. If you get hit in teams, chances are the opposing team can proceed to team combo you while keeping your teammate in check or at least make it difficult for them to help. Yoshi's defensive game takes time and needs plenty of "personal space" as well. If you've got multiple people harassing you, it's much more difficult to prepare defensive strats and react to multiple attacks with powershields, lightshields, and supershields, depending on the situation, which you will likely have a tougher time reading into as fully as you might have to in order to be effective.
Yoshi partnered with a decently fast character is GREAT against high, low, and bottom tier teams. Top and mid are kinda difficult, though; the matchups are bad and these two tiers house most of the best team combo characters in the game, which makes life difficult. Other than that, he's not terrible, but I wouldn't choose him
first.
If you like to play Yoshi and want to do well in teams, play Peach or Zelda. They hit slightly softer on average, but KO more reliably, faster, and are better overall team characters. Zelda, especially, since she gives you two moves to use and lets you focus more on the game and less on your character.