This is so difficult to enforce. You're going to have people go door-to-door checking if houses are vacant? What if someone goes on vacation? States require legibility. The simplest way to enforce high land and property utilization is to tax all property.
In California, for example, you have reports of people who move and use their old home in the Bay Area for storage because they're paying the same nominal property tax rate from 40 years ago. If they were paying a yearly 1% tax on the value of their property (instead of <0.05%), they'd rent or sell it immediately.
Same deal in China, except more extreme. Property _is not taxed_, so there are/were a lot of people building apartments and leaving them vacant, waiting for prices to rise over time.
Neither of these situations serve the material needs of people today who need cheap, high-quality, and abundant shelter.
Plus, your vacant property tax proposal excludes the (500k+?) many empty bedrooms in occupied homes. If someone's kids have grown and moved out, their old rooms are now vacant. How many people simply leave these rooms vacant for years and decades? A blanket property tax increase would strongly incentivize the renting of these rooms.