"Jack of all trades" or "well-rounded" are probably the terms you're looking for. I'm also fond of "balanced," but then you need to specify you mean in terms of stat distribution or skill tree investment rather than power levels. "Average" is going to imply being unexceptional rather than exceptional in a well-rounded fashion, as we've seen.
Elder Scrolls games have a shot at this, since your skills often don't compete with each other. You can focus on lockpicking to a lesser or greater extent while still getting use out of it, for example, and more importantly do so without meaningfully reducing you Axe or Conjuration skill. Playing a character that "does everything" is reasonably common.
I'm sure there's other examples, but none come to mind at the moment.
More generally, this is a common theme in games where you're controlling multiple party members, since while the characters themselves are encouraged to specialize to hell and back, your party usually tends towards the mean. It can tank, it can heal, it can pick locks, etc.
It's also more loosely applicable to anything with multiple moving parts, like empire games, though it feels like those tend to encourage you to specialize fairly often. An empire with balanced gold generation and balanced research and a balanced military tends to feel like it lacks a particular way to win more often than it feels like a stable, well-rounded entity with advantages over its rivals.
Very, very generally speaking, games that allow a lot of player control tend to reward specialization and games that force a lot on the players tend to reward balancing yourself out. If you can stab a bunch of enemies and then retreat to safety to heal, having a glass cannon becomes more effective. If you can hire a glass cannon to shoot your enemies while you meatwall it up on the front line, becoming a full tank becomes more effective.
Conversely, if Acid Ghouls periodically ambush you on the road and losing to them is costly, gaining acid resistance and the undead hunter perk becomes more attractive, even if you're normally fond of hunting Fire Boars and so lean towards specializing for such.