Yeah, but if you're willing to admit that these values are not universally or uniquely held by Americans,
what is the problem?
If the Average American only holds 6 out of 10 of your imaginary Core American Values, what does it matter if we invite in a hundred million New Americans who also only hold 6 out of the 10, because they were from a different culture? Where is the assimilation problem?
(Also, "free market capitalism" and "skeptical of government intervention"? Really? Are you living in a bubble or just willfully pretending that the last 100 years of American history don't exist?)