If D&D capped at 12th level, it'd be fine. You're looking at a max of 3 attacks regardless of source. That works well enough. You'd probably need to strip things like Improved Divine Smite from Pally 11, Brutal Critical from Barbarian 9 (IIRC), various Ranger 11th level options, etc. to address the extra 3rd attack from a pure class build.

It's that tricky game space from mid tier 3 on up that keeps us from having nice things. 13+ should be considered epic tier play, and have it's own warped ruleset and better guidance for DMs and their own campaigns. This would grant a graduated campaign structure, where newbie heroes start at 1st level and progress to 12. Veteran heroes start at 3 and progress to 12, and epic heroes either start at 13, or continue from a previous campaign, but with a definitive cut over that pushes them from heroic to epic.

A complimentary book might provide a smooth progression from 1 to 20, for those who want to go that route, but it wouldn't be the expectation for the average campaign.