These tax measures, as well as other parts of Hamilton’s financial plan, were not un-American. Nor were they explicitly designed to benefit existing capitalists, but to restructure the American economy and refocus capital on the manufacturing sector. Hamilton correctly identified that by refocusing capital on the manufacturing sector and increasing trust in US bonds, he would be able to build a more prosperous nation.
In having the Treasury assume all state debts and paying them back at current rates from tax revenues levelled against domestic product, and not discriminating between original debt holder and speculator, Hamilton was able to boost the newly formed nation’s international standing.
If he had carefully picked which debts to pay off, for example, debts to veterans and merchants, while leaving debts to capitalists unpaid, nobody would have ever paid a decent price for a US government bond in the future. He would have eroded the faith in the American government’s borrowing. He had to devise a debt repayment system which paid all debts, irrespective of the fact that by then, many speculators and existing capitalists stood to profit from the plan. 
Hamilton was also determined to build a manufacturing economy that was competitive on a global scale. For this, he would need the capital of existing capitalists. Without their buy-in, he would not be able to build the stable economy he knew was essential to the nation’s future prosperity. 
This is why his taxation policies were designed to benefit large businesses over small artisanal firms. By consolidating the market, he could increase American competitiveness and increase exports. While this may have destroyed small businesses in the short term, in the long run, it increased American prosperity.
Through this lens, the economic incentives and taxation features of his financial plan were designed to stabilize the economy, not benefit existing business owners. In fact, Hamilton found speculators and existing capitalists a necessary nuisance. He needed their capital, but his objectives, of keeping the value of securities high, was often at odds with theirs.
The idea that Hamilton was un-American and did not want to promote social mobility is laughable. He was a product of the American dream. He came from nothing to become the nation’s first Treasury. He wanted to build a system in which people with ambition, like himself, could rise to the top, and dedicated almost his entire public life to realising this system.
Also, the idea of upward social mobility had not emerged as a core American principle. The founding fathers had no issue with inequality. There is almost no reference to inequality and equal opportunities in the Constitution, beyond the commitment to "general welfare" which is not explicitly defined.
Upward mobility in America was easy to achieve. As lands were stripped from the Native Americans, there were ample land resources to monetise and population growth was slow. It wasn't a core value of American ideals because it didn't need to be. There was an abundance of opportunity for those who were willing to work.