You started with the idea that "Many state boundaries make no sense." I would argue that every state boundary makes a huge deal of sense given the context of its formation. Check out the History Channel "How the states got their shapes" program for passable discussions of why those boundaries are there. The national boundaries should also be a bit redrawn in this concept as well.
In your "Mojave" state, you show a relative backwater (Barstow) as the capital instead of much more populous places like Las Vegas (or even Ridgecrest!). As an aside, there have been occasional rumbles about merging portions of Kern, Inyo, and San Bernardino counties into one "Desert" county for many years. It never happens, even though the desert counties are all treated as uninteresting appendages on their host counties.
Note that any state or combination of states can merge or split as needed if their populations agree to it (it's fairly straightforward to push such things through Congress if needed). The fact that the state boundaries have been relatively stable for a long time is as much a testament to the huge voting blocks concentrated in cities as to anything else. There are far too many entrenched interests who fight tooth and nail at any suggestion that their power base might be changed for much to happen.
County boundaries are interesting. There were some articles some years back that suggested that the size and general shape of a county is largely related to the amount of ground that a law enforcement official can cover in a day. Thus, older counties and counties in tough terrain tend to be smaller, with larger counties generally farther from initial settlement. The same is broadly true of states.
Just sitting down and drawing boundaries on map is an interesting exercise, one which is vaguely similar to the results of regional variations in speech patterns. However, every boundary that we have today is usually the result of significant historical compromises, compromises that won't much show by just drawing boundaries on a map.
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