I just assumed that it was part of making your secondary stats important. Strength is a secondary stat for a rogue. If you want to have decent charge attacks and opportunity attacks, and to synergize well with a warlord, put some points into it.
Just charging you a feat seems like the feat becomes a "must have." It also seems like the feat would be sort of too good- it turns an entire ability score into a dump stat, honestly. What other feat does that? But then again, they made a feat like that for Swordmages, so who knows what we'll see in the future.
I do kind of like the OP's solution. Using an at will to obtain this ability seems like a more "real" payment than just spending a feat. I probably wouldn't make it work for ALL basic melee attacks, though. I'd make it work for opportunity attacks and basic melee attacks granted by a power. Then I'd give it something else extra besides just 1[W]+Dex. And I'd do the same thing for charges, except I might make that a pair or trio of encounter or daily powers. Some already exist, in fact.
So, OP, what about this?
VICIOUS REPRISAL--- Rogue Attack 1
You attack using finesse rather than strength.
At Will; Martial, Weapon
Standard Action; Melee weapon
Requirement: You must be wielding a light blade.
Target: One creature.
Attack: Dexterity vs. AC.
Hit: 1[W] + strength. Increase damage to 2[W] + strength modifier at 21st level.
Special: You may use Finessed Strike in place of an opportunity attack or a basic melee attack granted by a power. If you have combat advantage, you may deal sneak attack damage with this attack even if you have already dealt sneak attack damage this round.
Now it accomplishes a couple of different goals.
First, it gives you something to do with opportunity attacks and extra attacks granted by a warlord.
Second, it has a purpose other than just being used for opportunity attacks and extra attacks- you can use it when you have already used your sneak attack for the round. For example, if you've used an action point to make an extra attack, and you want to deal sneak attack again.
Third, it doesn't replace strength complete. Strength is still useful for charges, and its even useful (though not mandatory) for rogues when they use this power. If strength isn't involved at all in this power, it moves another step towards being a dump stat. This version will see use by dex/cha rogues who want to dump strength, but also by dex/str rogues who want the extra advantages it grants.
I don't know if its balanced, but its a thought.