Why Would a Conservative Support the State and Local Tax Deduction?

In this review of the tax proposal by Senators Marco Rubio (R-FL) and Mike Lee (R-UT), Amity Shlaes and Matthew Denhart criticize rolling back the deduction for state and local taxes without pointing to any reason at all.

Why exactly?

I know why liberals might support this deduction and oppose rolling it back. State and local taxes can be a lot more regressive than they might think best, so allowing them to be deducted from more progressive federal taxes (which implies that the difference in revenue to the federal government is made up for under the more progressive rates) alleviates that burden somewhat, among other more mundane reasons for it.

But what it also amounts to is low-tax states and localities subsidizing high-tax states and localities, so I don't know why conservatives would oppose scaling back this deduction or eliminating it.

I mean sure, if you're Grover Norquist and any deduction rollback or elimination counts as an impermissible tax increase even if coupled with other provisions that are revenue-neutral at most as a whole, then I see opposing this. But apart from such dogmatic purists, why would a conservative, who wants to simplify the tax code by getting rid of market-distorting deductions and use the revenue to cut other rates or shrink the deficit, oppose cutting back this deduction? If not this deduction, then which one? If not this one, how can they support cutting back any other deduction, a substantial number of which they need to identify in order to square the circle of their budgetary aims with regard to other tax cuts, the deficit and debt, and other spending?

To be fair, I'm not familiar off the top of my head with the details of these two's preferred options for tax reform, but I'm going off of the general conservative position on the budget which requires finding deductions to cut to be at all plausible and from which they haven't loudly dissented when it's mattered. That said, I will look at their ideas in detail soon. Also I think this highlights the problems that arise from the perfectionism of even good faith policy wonks, so many of whom have their own idiosyncratic favorite policy proposals and get too bogged down in the details to realize that such diversity and specificity of views, especially among the type of smart, invested and often contrarian people who participate in these arguments, is an obstacle to developing the consensus necessary to make real world progress and actually get something done.