So true that there are better peaks than Elbert in Colorado, better peaks than Wheeler in NM, better peaks than Guadalupe in TX and, dare I say it, better peaks in AK then Denali. Most of my favorite hikes and climbs to date have come on non-highpoint mountains, though I've definitely had some great experiences on HPs as well.
Visiting the highpoints, be them state or county, doesn't always bring about the best or most-challenging nature experiences, but they do bring a community of hikers/climbers/nature-lovers/what-have-you together around a common interest. A great idea would be to climb the most difficult mountain / hill in each state, but debate would rage on for years about how to put together that list. The highest natural land in each state is relatively easy to identify (exception: Michigan) which has allowed for the creation of this unique highpointing community. Access difficulties will always be around (coming from a county-highpointer in the vastly-private state of Texas), though I think if you talked to Scott Surgent, you'd find that gaining legal access to Eagle Peak in Hudspeth Co was one of his happier moments. The challenge in getting to the state summits isn't always based on physical fitness or ability.
I'm rambling again, how does this always happen?
I must conclude by saying that Driskill Mtn in LA is definitely the best-good mountain in the state!