How levels define D&D

[mmadsen]

Point-buy systems can break if characters are free to really concentrate their advancement in a single area, where levels force some spread of the effects of advancement.

Exactly. Not only does a class-level system enforce thematic consistency, through its classes, but it provides portfolios of abilities balanced against each other.

Levels don't cause there to be major differences in power. It seems to me they are instead a result of wanting to have such a breadth of powers in the game.

I don't think D&D's power curve was thought out in advance. I think the designers stumbled across the idea to give a "hero" four hit dice, like four units of ordinary men, and the fighter's power curve just followed.

Similarly, the designers made up interesting new spells, assigned them a level, and the magic-user power curve just followed. The designers weren't particularly concerned, going in, with the threat of an invisible, flying, death-dealing wizard; it just happened.

You can see Gygax try to deal with some of the "abuses" in later adventure modules, like D1-2-3, where various spells don't work properly in the proto-Underdark, special new monsters have unusual immunities, and so on.