TL;DR taking properties off the tax roll costs the remaining taxpayers more. Pretty basic stuff. I've been talking this up to local electeds for decades, with very little progress. The only success I've had is ending the local program that makes "historic" properties tax exempt, but the huge whale exemptions for hospitals and whatnot remain.
Although they key thing here is that it's not just that effect, but emergent unintended consequences. In the article, it describes how non profit healthcare institutions have an incentive to buy for profit clinics, because (alongside the other incentives), when they do so, the real estate becomes tax exempt because now it's owned by a non profit, even if the work being performed stays the same.
Only if you keep the things those taxes were paying for. I have no public roads anywhere near me, ~no police, no fire service, no public utilities, basically no county services -- maybe it is not for everybody but once I experienced it I would never go back to having these public services. I basically pay a pittance for the local school and that is it. Once property taxes are eliminated the other voters can push to not have their taxes raised and just shitcan what property taxes were paying for.
reducing or removing property taxes for legitimate historic properties seems like a good thing to me. I don't want every community to look like a slightly randomized version of every other community. Historic stuff is interesting. If we can encourage it to stay interesting and not get torn down to build a TGI fridays that sounds like a good thing to me. How much did your crusade to tax local historic structures save the average taxpayer? How many of those places will be lost?
Universities are just as bad or worse on this front. They will buy up properties with no plan simply because they have the cash to throw around and don't have to pay tax.