The NATO role should be replaced by European Union to disarm Cold War feelings. Take US off game can help to give another NATO image.
The lesson from the Ukraine invasion is that NATO is a stabilizing force, which keep deranged Russian leaders from invading countries and the members from attacking each other. So I see no reason to mess with a winning formula.
Indeed, there is no need to mess with the winning formula right now. Removing the US out of the equation also weakens the alliance to the point of making it more vulnerable overall to pressure from Russia. EU vs Russia is much less unbalanced than EU+US vs Russia.
Of course, Ukraine in the EU makes quite a considerable difference in this regard...