I do understand your comments about Kansas. I really do.
Nonetheless, my statement “Getting rid of the deduction will put pressure on these states to LOWER their taxes” is most likely true.
States with high state/local taxes will feel pressure to lower their taxes from their residents. In the end, the residents will get to decide, do they want lower taxes (with cuts to services) or do they want higher taxes (with more services).
The people of Kansas voted out “tax cut supporters”. It is their right. In doing so, they can have higher taxes with more services if they want them. Each state gets to decide.
Probably, as long as the people in the state don't want their roads maintained, their schools funded, their state police and prisons funded, and great grandma's retirement home paid for.