Why would the King's want a soft injury prone player like Hemsky, and why would they want to overpay for him?
Because he'd improve your 1st line considerably. He already has good chemistry with Smyth, and I think his game would compliment Kopitar's quite well. Neither of those guys are good skaters, Hemsky flies out there and dangles at top speed. With Smyth parked in front of the net and the combo of Kopitar's and Hemsky's one-on-one skill and passing, that is a dangerous line.
As far as the injuries, yeah they happen more than anyone would want to see, but nothing chronic. The guy has just had some bad luck (you know, like hit by Handzus from behind and landing shoulder first type of bad luck).
And as for your soft comment, I've never seen Hemsky shy away. Most of the time he gets run by a guy he gets pissed off and starts dishing it out himself.