This doesn't have to be true. Washington State, for example defines the amount of property tax revenue to be charged and then divides that in proportion to everyone's taxable value.
So if everyone's value goes up 40% your property tax bill stays the same. If your area climbed faster than others, it goes up but not by 40%.
If property prices increase 40%, then cost of living increases, government needs to collect additional revenue to pay employees a living wage, and that feeds into taxes. Even without higher order effects, the above chain was literally about net increases in property taxes to fund more services and saying it's fine because property values increase (in specific locations, too). But property values are not a tangible thing for anyone who doesn't want to sell.