I've had a Wii for just under a week, now, and, I'm sorry, but those people must be going absolutely nuts with their Wii remotes. For one, I don't see how the wrist strap would wear that fast unless you weren't actually using it properly (there is no tension/friction at the point where the strap is connected to the control for me - I wonder why that is. The idea is that the strap stops the control from falling/being thrown if you happen to lose your grip, which, as of yet, hasn't even come close to happening for me).
This kind of information makes me question how people are using their Wii remotes. Whenever I'm using the remote in, let's say, LoZ: TP, there's never really any risk that I'm swinging it hard enough to cause the kind of tension that would wear the wrist strap's connection down to nothing. Heck, the only tension on the wrist strap, for me, is the insignificant amount generated by the fact that the strap is draped over my wrist. That's hardly excessive. The same goes for Wii Sports - if you're actually holding the remote properly, there shouldn't be any tension/friction on the strings connecting the strap to the remote.
It would be nice to have a bit of a stronger fastening between the strap and the remote just in case someone isn't firmly holding the remote, but for me, personally, it makes no difference - I'm rather careful, and I keep a firm grip on the remote. Then again, the strap can be removed, and you can use any other variety of fastening and wrist strap to keep it on - you aren't obliged to use the one Nintendo ships with the console.
EDIT - Also, with particular emphasis on the first video (the guy playing Wii Sports tennis, I believe, on the wall-mounted TV) - people are using an excessive amount of force, it seems. The remote is sensitive enough to capture that kind of force in a much more gentle motion. I wonder if he read the manual...
