For 2 years, I lived in a suburb outside of San Francisco, that was primarily white. It was creepy and weird, coming from a large city suburb in Canada, including those in Manitoba, Alberta, and Vancouver. We also stuck out a lot, with a car the wrong colour and the wrong age (7 years old), hanging laundry in the rear yard, mowing our own lawn, driving "gasp" through the "bad" area of town (on a freaking main road/highway) to get to the city's airport, zoo, etc.
I think some of it was the greater populations in the US. When I grew up, you maybe had 5 blocks of "like" people living with "like", but the schools and grocery stores and workplaces were all mixed with several different ethnicities. In California, it was whole towns of 50 blocks of "like to like". Perhaps because the population is 10x larger.
The strangest day was when we drove to the nearby lake / beach park on a hot summer day. Typical cheap family day we would do at our previous locations. It was a maybe 15 minute drive from our heavily white population city/suburb, with mostly other white suburbs around. Out of hundreds of people, we were one of 4 white families, and there was only 2-3 black families and one asian family. WTF? It was like a sci-fi movie where we entered another dimension. It was a beautiful location with great friendly people, too. I still don't get it. At all. Why would people miss out on this fabulousness so close to them?
I have no idea why this happens, that people self-group en masse, other than perhaps due to the larger populations that exaggerate underlying collections.
I do believe that there are a lot of LCOL neighborhoods with like visible minorities in the USA, just as there are white LCOL towns.... So, maybe you just need to find them, and find one that feels right to you?
But IMO, you are correct to think that diverse (multi-racial) blended areas in LCOL can be hard to find, and worth paying a little more for to live in.