A more well-rounded overview of party composition would widen each character's niche to non-combat endeavors. That would look a little more like: Combat-Subterfuge-Spellcasting-Healing. All I've really done, of course, is give the Thief its proper due instead of making him sound like a Fighter who emphasizes damage over TAKING damage. Change the game, and you get different, if related, niches. In a Cyberpunk game, for example, you might have Combat-Decker-Fixer-Techie. In a superhero game, Brick-Blaster-Sneak-Controller and so on (you can of course have more than four roles, these are just quick examples). The point is, gamers will often think in terms of Roles and ask "What do we already have? How can I better serve the party, make it more diverse, make sure we survive and/or allow the GM to fully use the game world and system?" (after all, what's a Cyberpunk game with no netrunning, or good old sword & sorcery without sorcery? Even in games where there are no classes, players will still try to fill a niche, if only to make their characters more useful. In less combat-oriented games, this may be as simple as Body-Mind-Heart. But isn't there a point where this scheme hampers player creativity? Why does the fourth player on the totem pole (or last in character creation at least) usually have to make a sacrifice? And what happens when players miss sessions? Is the group then heavily handicapped?
Even since I got the Fighter's Handbook for AD&D 2nd all those years ago, I've been fascinated with the idea of running a Fighters-only campaign. But again, that book offers Kits that nudge the Fighter towards one Role or another. What about a game where everyone plays the same class and the same kit? Does that create a deep unbalance that makes life hard for players and GM alike? Much of my recent gaming has been classless. I give my players as much freedom as I can within the context of any given game world, and try to keep the emphasis on character rather than abilities. How do the characters connect with one another? How will they be entertaining to play, play with, or play opposite? What kind of plots and subplots can be built around their personal stories? I like to start with strong character concepts and build the campaign around them. And yet, there will be times when I want to bring in certain elements of the game world and find the relevant PC archetype missing from the group.
Finally, hand out a number of cards from the particular Role Deck to every player that has that Role. It should probably be 3 cards per player. If you have a single Role, all 3 cards will come from that pile. If you have two, one of them will be your strong suit (2 cards) and the remaining card will be from your secondary Role. There are many variations depending on the game and play style. You could try giving each player one card from each pile, giving them each the chance to play Combat, Healer, etc. in some way. Or the first card of any Role handed out could be predetermined by the GM to insure the scenario isn't an impossible one (always give a damage heal for combat-heavy games, or a trap disarm for trap-heavy ones, for example). You'll also have to decide if cards give session-long, continuous abilities or can played exactly once per session.
It might be fun for the Warrior to bully a wounded PC back to health or for the Wizard to cast a cantrip that allows him to hide in shadows, or whatever justification you give to the Role cards' effects. And in games where Warrior and Wizard are meaningless categories, it might be the only way to access certain abilities without dedicating your entire chargen strategy to acquiring them, to the detriment of your core concept. Just a thought.