Yeah, rechargeable batteries just die out after (hopefully) a while.
My first Wii recharger's batteries were dying out, so when I saw a good deal on the MadCatz one
I have now, I got it. Unfortunately, retail price is something like $40, at the time though I got it for $15.
It's not the greatest, as it uses NiMH batteries, as opposed to the better Li-Ion ones, but what I like about it is that it's inductive, so it'll work with the sleeves on for the times I'm with family with young kids, and it also works with or without the MotionPlus.
I can see the argument for rechargeable AAs. They'll probably last longer, and they're cheaper, especially if you already have a good charger for them.
However, I just find it more convenient to have a dedicated charger. I've got rechargeable AAs that I use in a number of things, but it's a pain if I have to take out the batteries from inside the remotes and charge them, when I really already wanted to be playing. And then if you have the sleeves on, you have to take them off to take out the batteries and put them back in, and I just find having a cheap set of Wii-specific batteries easier.
And since it's just a cheap set, I don't worry about doing a full discharge-charge cycle like you're supposed to do with NiMH batteries, and put them on the charger whenever I'm done. With my good Eneloop AAs, I'd rather not do that.