Sorry, but this is flawed logic.
Tech, more than seemingly any other industry I can think of, has a winner-takes-all model of success. Given this, starting a tech company anywhere other than where the overwhelming majority of the most capable employees live is virtually suicide. And this seems to pan out in the data as well — Twitter, Square, Uber, Google, Facebook, Reddit, AirBnB, Apple, Oracle, Box, Palantir, Pinterest, Lyft, Stripe, CloudFlare… not that these are all of tech, but finding even a fraction of these anywhere (other than perhaps New York) is a stretch.
Given that, it's patently worth it to pay the extra cost per employee, when the relative value of each employee to the company ends up being so high compared to other industries.
This is not to say you can't build a strong tech company in other parts of the US, but you're stacking the odds against you by doing so.