I really can't understand what you're getting so riled up about. It's not as if rerolling is totally worthless just because you might end up worse. In fact, in most cases you'll use your reroll to avoid certain disaster. OK, it would be ever-so-slightly cool if you could also make the best of a Craft roll with this - but in the end, that you can normally take 20 on, if it's really important, or get lots of Commoner followers to Aid Another, or whatever. Rerolls are for those situations in which you just wish you rolled less abysmal.
Having the option to reroll is
good. Simple as that. Your weak-ass Wizard rolled a 3 on his save against Finger of Death? Reroll, can't get much worse than this.
Your idiot Bard party member got a 4 on his Move Silently? Good thing he can reroll, isn't it? BBEG absolutely must die this round, or his next spell-like will kill most of your group: you got a threat! Oh, no, natural 1 on the confirmation roll... wait! I got my reroll right here!
Also, the 1/day thing. From mid levels onward, your Cleric or Wizard will get their best spell only 1/day. Often, you'll get a whole bunch of your spells only 1/day (cause you need variety when you prepare for the day). A 1st-3rd level Barbarian can use his Rage only 1/day, a 1st level Bard his music, a 5th level Druid his Wildshape. A healing potion is not even 1/day, it's 1/ever! As are many consumable items that you'll still have to rely on in many situations.
As far as the tactical aspect of D&D goes, it's a game mostly about resource management. You manage your hitpoints, class features, consumables, actions. If you refrain from using something that will make your life easier now, said life might end. If you don't use a 1/day power in a normal adventuring day, that day was either
less challenging (from the DM's side) than it should have been, or
more challenging (from your side) than it should have been.
What I like about 1/day powers and consumable items is the fact that they force you to make a decision. Decisions are interesting. Enjoy your decision-making!