Eh - that’s what we like to say to ourselves, but the first part isn’t true I think.
For instance, for pre-cap SALT to have resulted in a truly neutral federal tax policy, it would have had to not existed at all and have federal taxes be unaffected by state taxes.
Since it did exist, assuming a population has some fixed amount of taxes they consider ‘too much’ and all gov’t actors are looking to maximize towards that limit, it incentivizes states to take as much as they can, since the federal taxes ‘give way’.
The cap basically says ‘eh, we’ll let you do that, but only so much’. The ‘how much’ just so happens to still benefit their constituents while not helping their opponent’s constituents.
Which yes, has those effects you are stating, as their constituents tend to be more rural, which tends to have less economic activity in general, have lower incomes, etc, and hence aren’t hurt in the same way.
Though many of their donors tend to have higher incomes, and I imagine it took some convincing that it was worth taking a potential hit to ‘stick it to the libs’.