The US is quite a different case. Firstly, it wasn't feudal, wasn't roughly medieval, had access to much better agricultural technologies (and slaves), and most importantly, had a ready consumer demand that purchased the majority of its excess production (England) as opposed to having to internally balance a supply/demand cycle. It was also a situation of expansion into a previously unclaimed and fairly uncontested land (well, relatively, of course).
And, although I'm not an American historian, I think you'll find that those numbers are (effectively) artificially low because of large territory "purchases" from other countries. Territories that could only in the fanciful dreams of colonial states be claimed as part of the actual country until a much later time.

From 1790 to 1820 the sq. miles of land doubled and total population increased by 2.5 times. Land sq. miles had doubled again by 1870, but population had increased four-fold from 1820. Had there been no territory purchases, density would have rapidly increased, even though the land/population growth feed-back cycle would have been absent.
joe b.