In a vacuum, sure, but it would also discourage vacancy, which increases supply and thus puts downward pressure on rent prices.

I've heard of landlords artificially decreasing supply as rents go up so they can maximize profit per unit, or at least maximize expected rents to allow for better terms on loans (see NYC's insane real estate market). This would penalize that.

Also, property tax is often a progressive tax since it's based on value, not consumption. Many states get most of their revenue from sales taxes, so a state level property tax could replace a sales tax, which is notably regressive on the poor.

It would discourage home ownership and probably encourage more dense housing (reduces taxes per housing area), which is a lifestyle change but probably better for urban planning.