Missouri is neither stellar nor terrible in terms of auto transport. There are certainly enough people in the state to attract drivers, but because of how Kansas City and St Louis are positioned they hurt instead of help the smaller cities. Of course, anybody along interstate 70 will have an easy time shipping their cars, but anyone too far north or south of the road will most likely face problems as these places are sparsely populated and carriers rarely pass through. Interstate 44 can be simple to ship from depending on where you are going; Texas and Los Angeles are good but the east is usually tougher. Personal shipments are a huge portion of the auto transport into and out of the state. The economy is mostly based on aerospace and heavy equipment manufacturing and farming, it is not conducive to auto transport. Missouri is somewhat well positioned however, the mean center of the US population is here and interstate 70 and 44 are important national highways.
Missouri’s auto transport is heavily affected by snow birds. Winters are very snowy and many people prefer to spend their winters in warmer states. Missouri snow birds will primarily choose Florida but southern Texas is also a popular destination. When all of these people ship their cars between October and December the prices skyrocket going anywhere south but become extremely cheap in the other direction. At the end of winter, between April and May, everyone ships their cars back, the pricing effect reverses and transport becomes very expensive from the south to Missouri and other northern states. Try to ship in the opposite direction of the crowd or outside of snow bird season.
If you are shipping from a small city in Missouri waiting for a good price is pointless. Pay well enough so a carrier is willing to make a detour to pick up your car or meet off of the interstate. Everyone else is in a good situation and transport should be easy.