I stated that if they came to America via your suggested path, they'd be locked up for doing something illegal.
Insisting on "legal route only" when the legal route is closed is just a conscience saving lie.
"""Neither the 1951 Refugee Convention nor EU law requires a refugee to claim asylum in one country rather than another.
There is no rule requiring refugees to claim in the first safe country in which they arrive."""
Regarding "This isn't the US's responsibility..."
There are two answers to the "This isn't the US's responsibility" assertion.
One is that it's everybody's responsibility, and the US has the resources to shoulder a disproportionate burden (to say nothing of a bit of causal history creating the need to shoulder a burden in the first place; the US has intervened in South American politics for decades, sometimes with the express goal of disrupting the will of the people and local governance). Where others say "Why?" we should instead say "Why not?"
The other is that the country that has a statue in one of its largest harbors declaring "Give me your tired, your poor, your huddled masses yearning to breathe free, the wretched refuse of your teeming shore. Send these, the homeless, tempest-tost to me, I lift my lamp beside the golden door!" ... has declared it their responsibility quite openly.
Thought experiment: place a teleporter from Xinjiang to just south of the US border. Suddenly it's possible for the oppressed Uighurs to escape and cross the border into the US. What happens to them?
I suspect they'd simply end up in a different internment camp.