Why not? The opening that needs to occur before you can use that maneuver is just even more rare. So rare that it only seems to happen once per day.That might be a decent answer for encounter feats with complicated trigger criteria, but still doesn't cut it for dailies, IMO.
I've had similar discussions about these aspects of 4E with a lot of my old-timer friends. So I'll ask you the same question.
Image that all fights are five rounds long and you always manage four fights every day. Let's also assume that you have three classes of maneuvers; class A that needs no particular opening, class B that needs some opening that is fairly uncommon, and class C that needs a serious opening that is very rare.
What if the mechanics for this was; at the start of each round you roll a d20. On 1-16 you can only use class A maneuvers. On 17-19 you can use class A and class B maneuvers. On 20 you can use any class of maneuver.
In this way you, as the player, would have no control over when these opportunities occur. Random chance will give you an opening and you can choose to exploit it. Your fighter can do that high-damage finishing move only when the dice roll his way. Now, statistically, this will allow you the use of class B maneuvers once each fight and class C maneuvers once each day.
Would this be a mechanism you could accept?
Now, just imagine that let the player control that random chance...