As bad as things turned out, without the "removal" policy in place, all the Indians would have died of Old World diseases long before the age of anti-biotics.
Perhaps.
But, "all of the Indians" would have been a lot of them.
I'm more than a bit skeptical that God would have allowed it to come to that regardless. Perhaps in the case of the more ruthless and blood thirsty amongst them. But I don't think so for the more 'benign' amongst the tribes. God has clearly reserved utter extinction for the very ruthless and blood thirsty throughout history.