Yes. While some dailies have a miss effect, some don't and missing becomes an even more frustrating event.
I've play-tested this house rule in the game I played yesterday night in my head and it worked perfectly:
A missed daily that has no "miss" effect is automatically regenerated after a short rest.
Using a daily power makes PCs want to take extended rests.
I know of this - this is why I collect scroll and potions and never use them. In computer RPGs, I hoard them and use them just in the fight with the final boss.
At the end of Dragon Age, my bard chugged down so many potions, it had to ask the dragon to wait while she went peeing.

Scarcity of resources make them more valuable - I tend not to use them, in case a better opportunity to use them present itself.
I do have a clever house rule here... but first, I need to say that most of the times, players can take an extended rest after a fight. I take an extended rest after every day at work. I don't have a problem with players always taking extended rests.
I love the idea of creating situations where it is not a good idea to take an extended rest - it enhances the stress of using dailies (or of extended resting).
Back to the clever house rule. If you can, remember your first level wizard in 2nd ed, when it missed its only spell and was scared of taking out its sling in case a monster would notice him, spit on his face from a distance, removing the last of his 1d4 worth of HP?
My house rule builds on the same mechanisms we used back then to deal with it:
Suck it up
What are your feelings on 4th ed and dailies?
Original Alot, from Hyperbole and a Half, which you should be reading.
Red Dragon from Dungeon and Dragon's 3rd Edition Player's handbook. Wuss adventurer added on it by an artist I don't know.

Comments
If I were to house-rule it, I'd say that you can opt for your daily to go off anytime you roll a natural 20 (but keep it a non-natural 20 result). cringe Roll again to confirm the critical.
I don't know, it was just a thought.
-Tourq
Of course, I do make it hard for the group to take extended rests, so those surges are precious.
I honestly never build my characters to rely on my dailies, I use them for escape routes and some finesse to combat, but they deal about the same damage as my sly florish.
I've almost always eaten the cake I've had *grin*. (Seriously - if you don't want to eat cake, you shouldn't have any!)
I don't think the house rule handicaps the dailies all that much: you still get a chance to miss. If you do, you still can't try again during the encounter.
In the same vein, another "house rule" I used when playing with kids that was popular was allowing them to re-roll a roll they missed.
I equipped them with a each with a "magic luck stone". When they were displeased with a roll, they could invoke the magic within the stone and re-roll.
The stone then crumbled to dust.
Made for very interesting scenarios where a player gave his stone to another player who had missed his power (they had not yet unlocked their daily powers - a simplified DnD intro game).
I feel strongly that reducing frustrations greatly enhance the game.
Reducing - not eliminating....
After all, triumph without peril brings no glory.
@Eric: And don't forget the Artificer! Recharges your item dailies!
I definitely feel for you when you say that players don't use their dailies enough. I'm guilty of it myself as well unless I make a conscious effort to use them. However, it just feels to me like your suggestions come from wanting your cake and eating it too.
If you can't handle the risk of dailies, you shouldn't get the reward. Either have dailies that (almost always) are available daily, or don't.
That being said, it's a game, and a game should be fun. One of my DM philosophies well-known among the Gamers' Syndicate is that if you want to cheat, I won't stop you. If you actually are capable of having fun rolling critical hits every single time, then have your fun. The most impressive feat of game design for 4e is that it insulates non-powergamers from powergameres, and cheaters are essentially just super-effective (and lazy) powergamers (min/maxers, whatever). What you (and others) have suggested certainly doesn't rise to this level, so I could accept that as well, even if I'm a player on your table and didn't give myself that benefit.
I'm not the slightest bit frustrated by the mechanics of 4e but hold nothing against those that are.
In complete agreement.
(still liking the house rule :P)
Yeah - the Warlord! This is the class that has the daily recharge power that is so awesome!
The house rule, as it stands (even in its rewrite in the comments), aims not to overpower or step over its bounds : if you miss your daily, you miss it.
Regaining it after a short rest instead of an extended rest - only if it missed in the first place - is meant more as a soothing bounds. Makes dailies more powerful, yes, but encourages their use.
I think the end result will be subtle, as most encounters give time enough for an extended rest if needed anyways.
In the few games we played (always low-level), I remember only a handful of times dailies have been used. I want us to use them more.
(How many dailies fit in a hand anyway?)
The fact that missing with a daily is full of suck, and hitting is full of win, does two things: 1) it creates dramatic tension whenever you're rolling for one, and 2) it encourages strategic thinking and teamwork to stack up those to-hit bonuses. Making a daily less daily makes them less special.
-- Cameron McNary, Artistic Director, Critical Threat Theatre
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