Again, I think you have to look at the outcomes. Every German and Austrian Jew who wanted to leave Germany and Austria in the 1930s did. Including Anne Frank's family. This was well before extermination crossed anybody's mind.
The Western democracies embraced the Jews with open arms. Some of those Western democracies later fell to the Germans, but nobody could have anticipated that. Now you can argue that more Jews should have come to the US and the UK instead of France and the Netherlands, but that's a judgement we can only make with the benefit of hindsight. Nevertheless, a great many Jews did go to the US and the UK.
Wouldn't have been substantially different, though a large number could have been saved. Palestine could have been far more important that 70,000 or so unused immigration slots to the US.