You're assuming that the US doesn't respond to political pressure and come up with an agreement with the EC to enable the flows. The wiretap act already goes beyond the fourth amendment in protection.
The problem is the European Commission is not applying political pressure because it rolls over for every fig leaf the US offers. It then takes Max Schrems to sue and several years before the CJEU overturns the "compromise".
That said, the Biden administration's latest proposal might pass muster if the proposed redress mechanism were truly independent as part of the Judicial Branch of the United States as opposed to the current proposal which is still part of the Executive and thus conflicted in ruling against surveillance decisions of the Executive Branch and its agencies:
That said, even US citizens don't enjoy meaningful protection against warrantless wiretapping that clearly violates the Fourth Amendment due to the deference the judiciary has given to the executive, so I am not optimistic.
