In my limited experience, it doesn’t happen all that frequently, but not for the reason you’d expect (no excess claims) but instead it is infrequent because few people buy the coverage. It’s optional in most jurisdictions and nobody wants to pay more for their coverage. Most jurisdictions have low liability coverage limits. A PI lawyer will see many injuries in a career that exceed the limits of the defendants coverage, but if the client didn’t buy UIM coverage, he’s SOL. 
Many states had a surge of claims because of a weird change in policy. States changed their insurance laws to require insurance companies to offer UIM to their policy-holders. Cases held that if the insurance company didn’t make the offer, the policyholder automatically got coverage. So a bunch of people hit the jackpot because they had UIM coverage, for free, without even asking for it.
I wrote the briefs for this case (we lost on statute of limitations grounds) http://www.hsba.org/htdocs/hsba/Legal_Research/Hawaii/members/ica/19865.HTM which dealt with such a forced policy.
The case was complicated by the fact that I didn’t have an actual policy in hand to base aruments upon.