Thanks to Dave of Critical Hits, I have found some holes in my “no more ability checks” idea.
Making Bull Rush an Athletics check steps on the toes of at-will forced movement powers like “Tide of Iron”. A Fighter trained in Athletics would actually find it slightly easier to Bull Rush than use “Tide of Iron”. The only disadvantages would be the lack of damage and the lack of marking.
But this is not the kicker. This can be accepted and dealt with, especially for powers like the Warlord’s “Opening Shove”, which allows an ally to shift or make an attack.
Rule 42. Actions the rules don’t cover. Ability checks come in during some of these, as attacks without weapons are essentially ability checks.
Trip: Strength attack vs Reflex
Throw sand in their eyes: Dex vs Fort
So, unfortunately, ability checks can not be completely done away with.
(But the little boxes on the character sheet that people keep confusing with their damage bonus, or vice versa? Yeah, that can probably be removed. Or at least moved away from the ability scores box.)