That works, though it scales off the edge in paragon and epic tiers unless you also scale up the rp benefits (which I probably would anyway). Aurance, it's pretty clear--PC's players can either get a hit bonus for good description, or pay a feat to always get a flat hit bonus (but then never get a bonus for a good description).
Mind, it's not hard to optimize for mitigating bad luck (aside from the obvious case of "be a rogue"). Area attacks are great for this, as they tend to grant you multiple rolls even more than the Avenger's double roll does -- in exchange for less target choice, natch. Or the obligatory Avenger multiclass, and in high heroic/paragon, Stone of Foo(which combines amazingly with said Avenger multiclass), the Luckblade (daily reroll), Dice of Auspicious Fortune (merely overpowered if you rule that they reset to 0 after 24 hours, not broken), a lucky charm (free action +d6 to a d20 roll), having a friend who is an artificer (recharge a daily every milestone or get a free action +2 to an attack roll, usable when you need it). Then there are the marginal (but stackable) hit bonuses -- back to the wall, Dancing Thorn Style, and so on.
Or you could build a character who doesn't much care if she hits or misses; go with hammer, take all the "+strength damage on a miss" powers, and ignore the d20 except on a critical. Sure, your damage is usually uninspiring, but it's respectable, and you're fairly cheaply freed from the chains of the dice on one aspect and can then optimize to cheat fate for enemy attacks or saving throws.