It depends on what you're counting and when you're counting it. But the US has the best land in the world for growing corn and cotton, among the best for growing what and rye, and has almost any mineral resource you can imagine.
When you're counting it: once the prairie is fully colonized, once the mountains are all explored and probed.
Estimated date range for that eventuality: early-mid 20th century.
That is like saying the Russians are making a wise move in settling Siberia because Siberia is where all the uranium and oil is. Yes, it's accurate, but it's not something the people in 1820 know about, and it's also fucking worthless to them when they're planning for events twenty years down the line. And it's so far beyond the point where America's population literally makes Britain a minority in its own empire that there is literally no point in planning for it anyway. If there is any pretense toward common democracy between America and Britain, that's just unavoidable.
There's a reason that there US became a behemoth,
That reason being its industry and its population size, and the fact that its industry grew the fastest in the world in the late 19th and early 20th century, not its resources.
and it's just not logically consistent to say that it's simultaneously a worthless barren wasteland and also so wealthy and powerful that it's going to eat the Empire.
At the time, it's far from that point, and most of the factors that you mention aren't even visible yet to people planning at the time.
However, the industrial and population growth in America very much is
visible, and it's very bad for Britain because this American majority is going to become the economic center of the empire by virtue of being the place where the industrial and population majority will be soon enough.
Compare that to India, which is more populous, but the locals also don't have the right to vote and don't get uppity when their civil rights are infringed upon (it also helps that they're brown people with no connection to England, unlike the Americans). While India is much less industrialized than America, it also has a lot more commerce moving through it at the moment, and that commerce is much more easy to tax and re-tax than America's is. So India is just naturally a more lucrative colony in the early 19th century, and less of a problem to the empire in the latter 19th.
In think in general, you've got a valid argument, but you're overstating it. Like, it seems inconceivable that the British wouldn't have renegotiated this trade relationship with the American colonies in the wake of subduing the Rebellion.
They would have certainly tried, and they might even have partially succeeded for a while. However, there is still
the fact that Britain is going to be increasingly marginalized in its own empire just by the fact that America has more space to populate. Giving them seats in Parliament would actually make this very plain to see, as every decade there are more and more MPs being added from the colonies.
There is simply no way that London will willingly sign on to becoming the junior partner to America.
So that probably means more taxes *and* more representation in London. And that, in and of itself, changes everyone's math.
The colonials didn't just rebel over the taxation issue on its own, so much as the idea that their ancestral privileges were being infringed on by a government that wanted to standardize administration across the empire. They complained as much about additional(*) customs inspectors and anti-smuggling operations as they did about taxes or representation. They thought that a few thousand troops
stationed across the Thirteen Colonies could only possibly
be there because of some secret plot by the government or to enrich the commanders, not to protect them and supplement their severely-lacking militias against the Natives. In every act the British government did, they saw the hand of tyranny moving against them, or so their propaganda went.
Point being, this is a more difficult problem to solve than you imply. American and British interests will come to loggerheads eventually, and it's only by luck that the Americans will stay in the empire for even a century longer.
(*): and, most importantly, less corrupt customs inspectors that wouldn't just let the rampant smuggling and bribery go unchecked.