The first superhero game I played repeatedly was Champions. Champions, like D&D, encourages tactical play, so teams tend to have types: there's the lots-of-damage-melee guy, the damage-at-range guy, the hits-what's-hard-to-hit guy, and the oddball, who either does damage to folks the others can't touch, or has some sensory thing that the others can't duplicate, or works as a support person. Your fighter, your wizard, your rogue, and your cleric, in other words.
And in terms of gaming, that's certainly what I did for years and years and I don't even want to admit how old I am.
But that's not the way that teams work in the comics.
Teams, as I've said elsewhere, exist between one of two poles: the IP parking lot pole and the Peyton Place pole. An IP parking lot is a place to put characters just to prove that the Intellectual Property is being used; and Peyton Place is a foment of internal passions and discord. In the first, the villain is essential; in the second, the villain is, well, secondary and exists primarily to point out character things. ("This is why our love can never work, Moonsilver: Because you were not horrified when Amy Geddon said she wanted to kill everyone and start over...")
These distinctions are hardly absolute: the deMatteis-Giffen era Justice League tweaked personalities so that the interaction of the characters was primary and the villains were secondary, but it would be hard to find a purer example of an IP parking lot than the Justice League. On the other hand, the freshly-Kickstarted Masks RPG has a set of personalities and powers are almost irrelevant: what's important to the story is how the characters are going to react.
Most traditional games approach it from the tactical end. Each character has a role. In games such as Champions, the role is about what the character does. In games such as Masks, the role is about what the character is or how he/she/it reacts. A game with random character creation is more like an IP parking lot because you have no idea what's going to show up. It might be the burrowing guy with the magic staff, the interstellar cop with the light sabre, the speedster who has trouble hitting Mach 1, and the cosmically powered witch.
I assume that most players want something in the middle. They want something that isn't just tactical, but the idea that the villain is secondary isn't quite their cup of tea either. So how do you fit them together?
If you don't know what characters you're getting, maybe the answer is to take a page from FATE (and sort of Masks): Powers are irrelevant to working together. What they have are Aspects or disadvantages. The Aspects or disadvantages are crafted to make the team work together (or to create friction while making the team work together).
For instance, the X-Men all have the mutant disadvantage. It doesn't just mean that they show up on bioscanners that the bad guys have...it also means that the world hates and fears them, that there are strong social pressures to keep them with the group. Most of the X-Men are young, so they fit into the school setting. That's an example of social pressure holding them in place, and perhaps it could be gamed that way.
Did they ever do the road trip with X-23, Sabretooth, Logan, and his son Daken all trapped in the car for a long journey? Because that's pure comic book: that's four people with essentially the same powers but different ways of reacting.
Maybe you can use something like that instead of saying, "Hey, we need an energy blaster."
Or, like, you can re-roll your character until you get an energy blaster. Whatever works for you.