At least in the US, mortgages are typically fixed cost (I know this is not the case in many other countries, like the UK). You know when you sign the contract what your monthly cost will be, for the life of the loan. ARM loans are an exception to this, but ARM loans are nearly universally considered a terrible idea unless interest rates are egregiously high at signing time, or some other edge case applies to you.

Thus, you can budget around the mortgage payment in a predictable way, and if you have to move out because you can no longer afford it, that's a very different thing than if your property taxes magically change because a theoretical buyer may theoretically be willing to pay some astronomically higher cost for your house than you paid for it.

So, respectfully, I disagree with the framing that we have to take both or neither. They are separate budgeting concerns, and separate policy concerns.