I save > 60% of my post-tax income. I'm able to do this because, 1) luckily, I make a lot of money, and 2) I don't have any dependents or health problems.
If I moved to St. Louis, I'd save an extra ~$2k a month in taxes, which is basically the cut in salary.
I /only/ spend $40k a year outside of housing (I realize this is a lot). A lot of that /was/ on traveling to see friends and family, and about 10% of that is utilities, car payments, etc - things that don't really change. Let's say $20k of my spending is on local services like entertainment and restaurants and general shopping. Let's say that's 30% cheaper in St. Louis.
That's $6k in savings. Plus another ~$1-2k per month in rent. Absolute tops, that's $30k per year. For context (not to brag), this is not much much more than my annual raise.
Sure, if you have a giant house and several dependents, and spend ALL of your post-tax income - living in Saint Louis could offer you twice as much spending power.
For a lot of people, it doesn't. Most of their money goes toward investments, and I can't buy investments any cheaper from Saint Louis than I can anywhere else in the world.
Finally, if you own, even with the $12k limit on SALT, the fact that Mortgage Interest is deductible makes the difference in housing not as extreme as it might appear if you make a lot of money. Also, a lot of places with very high housing prices - unsurprisingly - have really low property taxes.