Point of order: that is blatantly untrue. Anti illegal immigrant has everything to do with ensuring the people in the country are known and allowed. It is completely uncoupled from legal immigration. To say an easy solution is increasing legal immigration is just saying lets leave all the security holes wide open and just make it so only the real bad guys use them because others have an easier time going legal.
You could keep the vetting system and still increase legal immigration a lot. Those are two separate issues.