Honestly, Thoresby has it right.
America's population was exploding all throughout the 18th and 19th centuries pre-industrialization, and the Appalachians aren't a big enough hurdle at all to stop westward migration - especially once the east coast is linked to the Mississippi watershed via canals, roads, and other waterways and footpaths. The population's simply way too big to not just stop moving west, especially with the mostly flat and fertile land east of the Rockies, and come the Great Plains, Anglo-Americans will begin ranching and they'll still drive Amerindians out for their cattle herds' safety. And Anglo-Americans were already reaching Texas in the 1820s and would've reached the Northwoods region (eastern Dakotas, Minnesota, etc.) around the same time if the Northwest Territory wasn't already organized ahead of time (small amounts of squatter colonists were trying to settle Ohio in the early-mid 1780s but driven out by the army until first official settlement at Marietta in 1788, slowing northerners' westward settlement patterns vs southerrners'). And Americans were already sailing to the Pacific coast to trade with California in the 1790s and claimed the Oregon Country in 1805 via Lewis and Clark - if they somehow gained full control of that land that early, you betcha that immigrants would push specifically to the Pacific coast to settle - decades early - and begin trading links with East Asia.
The future USA, barring most of its southwest, is blessed by the Intracoastal Waterway and many big mountain passes in the Appalachians connecting its land east of the Rockies in a huge natural highway system, land that ended up being is a truly gigantic amount of relatively flat, rich, and traversable farmland. And even the Oregon Country has several big mountain passes if need be to let Americans cross into the otherwise lovely and useful Columbia River basin. Even the southwest is easier to access from the Mississippi watershed and Pacific Northwest than Mexico if push comes to shove, and it is easily the most isolated, rugged, and non-farmable region within America by and far.