It never happens because it the math just doesn't work out. State/local revenues boil down to: property taxes, sales/use taxes, excise taxes, fees and income taxes. The big revenue streams are property taxes (schools, towns), sales taxes (county/state), and income taxes (state). Fees mostly sustain individual programs and have limited revenue potential - you can't make a fishing license $1000.
So when you get rid of property taxes, you get rid of local control of the levy, which sounds great until Little Rock doesn't want to provide state funds to pay your football coach $200k. Even in a middle of the road state like Arkansas, the pressure to meet Medicaid and other other state program dependencies would make it difficult to fund local government. You'll have a revolt if try to levy a 20% sales tax.
The talk radio answer is "shrink the government!". That means layoff cops, firemen, close schools and libraries, eliminate school sports and close public resources like parks, libraries and suspend things like street lighting. That will make reactionaries happy, but employers will leave.
Nonetheless, the content of what you said seems reasonable and sound. Thank you for helping me understand this.
[1] https://learn.roofstock.com/blog/states-without-property-tax