It's a lot more complicated than that. Different modes emphasize different abilities of characters. What is powerful in single player or match are generally very different things. Sonic is fast. His speed is powered by his ability, the thok, which gives you instant speed. His drawback is that he has a serious lack of ability to go up. Without a spring, slope, or other method of gaining altitude, Sonic is limited in his ability to go up and he cannot bypass any platforming at all. To take the obvious opposite example, Tails has absolutely no problems going upwards at all. His ability completely trivializes many platforming challenges and he can easily traverse complicated terrain with no real issues. Tails, however, can't go fast without a lot of prior planning. Without spindashing or speed shoes, Tails is stuck accelerating up to his running speed the slow way and runs slower than everyone else to boot. These strengths and weaknesses are practically polar opposites.
Now, let's look at two obvious modes of play. In single player, the emphasis the game provides is platforming and challenging terrain. Tails excels at that, and the single player game is by far the easiest to play through as Tails. In match, the emphasis the game has is on acceleration and speed. Sonic excels at that, and therefore he's incredibly strong in match. The designs of our modes emphasize different things, and different characters fill those niches best.
We could, if we wanted to, "fix" this by shoring up the character's weaknesses. I'm pretty damn sure that if Tails could fly around at run speed, he'd be way better in match. If we gave Sonic the ability to, say, thok directly upwards, he'd be way better in single player. The problem is that by circumventing character weaknesses, we make the character overall less compelling. The whole POINT of having a choice is to make you give up something for something else. If we removed those weaknesses all of the characters would be fair, but at the cost of making all the characters the same.
I think that homogenizing the characters would be a huge mistake. We want our characters to all feel unique. While this does lead to more complicated questions as to how to make single player challenging for Tails and how to make Sonic weaker in match, it's way better in the long run to preserve what makes each character unique, even if they're drawbacks.