It's not just evangelical Christians. I am Catholic and I know many Catholic parents who homeschool. My kids go to a non-denominational Christian school (primarily because there was no Catholic school in our area when my oldest was ready to start) and I have been very, very pleased with the quality of the education, the Christ-centered philosophy, and the dedication of the teachers and parents.
I have thought about homeschooling, but I'm pleased with the school and as long as we can afford it, we'll send our kids to private school. If we can't afford it, I'll homeschool. Public school is not an option.
I do think homeschool and Christian schools will greatly help our society in the long run; it will be these kids who will ultimately change the world because they answer to a higher power.
I agree, except that the transformation will take more than one generation to accomplish. The Left's long march through American institutions did not start with the 1960s hippie and antiwar movements, but in the late 19th Century with the rise of Social Darwinism, "higher criticism" of Biblical truths, and a materialistic worldview. They have taken over a century to take over; it may take another century to root them out.
There is also the possibility that a Baby Boomer or Generation X Lenin might arise should economic conditions, foreign wars, or racial tensions be sufficiently severe as to make room for a leftist strongman. Were that to happen, home schoolers and other conservative Christians would be among the first to land in an American Gulag Archipelago.
All of these matters are ultimately in the hands of DIvine Providence.