You can't ignore the fact that, statistically, those outside the U.S. and certain other countries have many attitudes and values we don't want to encourage in the U.S., at a higher rate than the prevalence of those attitudes within the country. Of course you can't impose ideological tests to get into the U.S. Which is all the more reason to limit immigration to what you can comfortably assimilate.
As an immigrant myself I'm really thankful for our melting pot policies. Life will be better for my daughter growing up surrounded by American attitudes. Had our family immigranted en masse with a million other Bangladeshi families, she might very well have been deprived of that.