UIM coverage also helps you if in that same situation, you have serious injuries. Best of my knowledge, it can apply to a passenger as well for a not-at-fault accident. It's way beyond what med-pay or group insurance provides. Example is the drunk who hits you with low liability limits (if any) and you or a passenger have permanent injuries.
To simply say "I'll sue the guy", good luck with that if he makes little money or just moves on. You're still stuck with the residual of a permanent injury.
To claim it, you act as a plaintiff against your own carrier to get that money. It isn't inherently a pretty process but if you have a permanent injury it can be very very helpful. I have 250k UIM on my two vehicles; the additional premium is negligible. Some might not agree with my approach, and that's fine and I certainly hope I never have to use it.
HTH