I disagree. Decades ago, when I was a poor young adult just beginning to make my way, I got those renters refunds, and they were nice -- but the amount was too small to actually make a substantive difference in my life.

Assuming that the amount of those rebates reflected a majority of the tax money collected for the property (just for the sake of argument -- I don't know that this is true), then eliminating that tax entirely would have an almost insignificant effect on housing prices.