As an option for occasional elite brutes this could be interesting. But I think the mechanic used will actually make the brute less effective in combat. The advantage of making two attacks over one is that it averages the rolls a little and makes the creature more likely to hit and do some damage (or provide a full hit / partial hit / miss system) with your system the creature either hits or misses.
A system that I like to use is the plain old 2 standard basic attacks but add in extra damage or an effect if both attacks hit. This can give you the spike damage you are looking for without increasing the chance of no damage at all.
Here is an example from a level 28 elite brute I recently used:
Sword Chop (Standard; at-will) Attack +31 vs. AC; 4d10+11 damage (crit 6d12+51 damage)
Double Chop (Standard; at-will) Punisher makes 2 Sword Chop attacks; if both attacks hit the same target the target is also knocked prone and weakened (save ends)
This reminds me of another aspect you can add to brutes to make them potentially more fearsome, critical hit damage. If every brute does more damage on a crit the players will learn to give them a little more respect.
Greg Bilsland suggests taking the flat damage modification after rolling dice and doubling it for paragon monsters, and tripling it for brutes. So 2d10 + 15 becomes 2d10 + 45 for brutes. Wow, I look at that number and it is terrifying.
I had a thought with your last comment - about not doubling the hit points.
How many XP would a monster with two attacks (i.e. elite) but standard HP be worth? 150% of a standard monster? 2 of these guys equal 3 standard monsters.