To address Yreka and Barstow as my capital picks, one: Yreka was proposed as the capital for Jefferson a long time ago, so I didn’t pull it out of my butt.
Barstow is at a key point on the interstates. If you’re coming from the east or northeast, you’ve got to go through there to get to the coast (unless you’re coming from the south to San Diego). It would make sense to place it there.
As for requiring a capital to be of a certain larger size, why ? I think putting them in a small town is better. People there should go for work and then leave to go home. Washington, DC was a literal swamp in early years. Nobody wanted to stay there for long and they were anxious to go home. As soon as it was civilized and socialized, it became an attractive place to stay. Now people go there and don’t ever want to leave, save for the few people still possessing their ethics and morals. How many people go to Montpelier and want to stay there for perpetuity ?
As soon as DC started exploding in growth in the mid-19th century (or post-Civil War), the U.S. Capital should’ve been relocated to rural central Kansas or Nebraska. A place that could only accommodate a modest population. Certainly not in Kansas City, Omaha or even Denver just because it was the largest available place in the region. That’s what you want to avoid. Founding Fathers (not just of America, but of individual states) knew that capitals were generally supposed to be secondary in size and in the middle of a state, otherwise they’d have kept them in New York City or Detroit (the original capital of Michigan).
I’ve been to Barstow, spent the night there (the day after fleeing the L.A. riots of ‘92). It’s dusty, windy and has tons of trucks and motels. It’s a perfect place for a capital to be to keep the people there but for a short time and to head home. Yreka is marginally better, and has interstate access, both important.
Your small capital reasoning makes sense to me.
Of course these poor towns might not want throngs of government workers to descend on them. ;p