Can a 400BBM w/cheap aluminum heads compete/dominate against the street LS?

Part of the trouble is, as brian6pak said, the ports is what makes the power. Plus the possible stout roller cam with killer rocker ratio, and a six bolt bottom end. Means far better breathing and power per cube, and lots of rpm. An ordinary truck 5.3 has way more power, and potential than a stock 400.
And, turbo kits for 400/440 are almost non existent, there are chinese turbo kits for a 5.3 ls than can almost triple stock output, for reasonable money. (Why i suggested a nitrous kit, they fit everything).
Dont get me wrong, i LOVE my big block mopars, and since i know nothing about the ls fuel injection, i will never do an ls. But i understand why they are the most popular swap around.
It sounds like you’re saying Big blocks are irrelevant on the street.

I am under the belief that most car people (HERE) don’t have that kind of money, but they do soup up cars, and additionally LS swaps ARE cheap.

I realize that out in California, & in the NorthEast/big cities that there are plenty of people that can reach above 800-2000 horsepower, I am not concerned with big money cars.