Be careful what you wish for. California capped property tax increase since 1978 with prop 13 and most experts say this is a major factor in their insanely expensive housing market. Most people are heavily incentivized to never move to keep their low property tax rate, but this in turn prevents most new development and upzoning while simultaneously leading to the worst sprawl in the nation.
It also starves the state of tax revenue requiring them to levy the tax further for new buyers and seek other income streams like heightened income and sales tax. Policies like this somewhat unintuitively only benefit those who are already well off. Renters and younger people gain no benefit and ultimately pay higher property taxes than those who already are financially established enough to own a property.
A healthy property tax disincentivizes housing as a speculative investment, improving the overall market for people who actually live there. There should certainly be breaks for poverty and financial distress but capping or cutting rates broadly encourages speculation. For a basic human need such high degree of speculation benefits nobody.