No, because the defense has been making that claim all along, so they should have submitted their evidence from the beginning. They're not allowed to surprise the government with "new" evidence that has existed since the start of the proceeding; real life doesn't work like a Hollywood movie.

What new evidence about the inhumane conditions of US prisons has come into existence since the start of the trial?

(Answer: COVID19, but that is only relevant so long as the pandemic continues, and would delay but not prevent extradition, which is why such evidence wasn't permitted at the hearing.)

EDIT:

Why then was the government allowed to swap the charges halfway?

Because (a) some of the underlying charges for extradition were changed by the US so they had to, (b) they didn't swap all of the charges and (c) the UK government only needs to show a prima facie case for one of the extraditable charges (based on information given them by the US), not all of the charges, and they already did that for one of the original charges and that charge is still part of the US criminal indictment underlying the extradition.

Note that because the hearing is a procedural matter, not a meritorious one, the magistrate judge would have the discretion to keep the case going even if all of the charges had been swapped.