Without the influx of new cultures and ideas, we become stagnate. This has been the curse of many burgeoning countries. Look at the countries that once flourished and are now without the bloom of their youth (UK, Germany, France). Once the input of new peoples ceases, death of their country follows thereafter.
(Will admit that my argument only bodes true if Islamic cultures are excluded.)
The US is a great example. Think how great this country would be if we had excluded the Germans, Irish, English, etc.? All their input was tantamount to making this country great.
As of the late 1700's according to the first census taken, the most prevalent ethnicities in this country were in descending order (German, Scottish, English). When we first voted on establishing a national language, Germanic almost won. So you could not have excluded the Germans even if you tried. Apparently the best we could do back then was deny them their language !
An influx of new cultures--and their attempts to survive here--does not help the country.
Except for cuisine--the exception because English/British food is so bad?