Well, you could get an education at Stony Brook as well, so while there is plenty to complain about in the US system, in your case, there are affordable options.
Also, Trinity College Dublin and UCD are a little cheaper than Oxbridge.
Also, most publics don’t offer good fin aid to OOS.
Also, NYU isn’t a public so doesn’t differentiate between OOS and in-state and tends to give poor fin aid anyway.
Finally, CMU and Brown aren’t rich. Compare their per capita endowments with HYPSM, WAS, Rice, and Grinnell. Or Oxbridge and Ivies/equivalents like UChicago/Northwestern/Columbia/Penn or WashU/Emory.