Why did the peoples of north america not achieve the population density of the societies of mesoamerica?

This might not be the only reason, but if you look at the map you can see a pattern: Mesoamerica is very narrow and limited by a desert in the North. At the same time, it's relatively fertile and people would not have a lot of motivation to leave, even if they had where to go.

North America is a lot wider and also less fertile (means that people would have an incentive to migrate) - this contributed to a lower population density.