It has advantages and disadvantages. In my city, abandoned property often gets saddled with old tax liens and cannot be given away.
Surely this means the land has a negative value, and should get a positive tax, seems silly to have liens that are > than the value of the property.
What state/country do you live in?
To put it another way, a property tax would be paid by the freeholder, not the leaseholder. This wouldn't make much of a difference for renters (as the owner would simply pass the cost on), but for owners of leasehold property it would be a stunning boon (and for freeholders who have sold the lease a disaster).
https://www.gov.uk/council-tax/second-homes-and-empty-proper...
Empty properties are not always exempted. It's up to the council. Sometimes they are, sometimes there's a discount, sometimes there's no discount, sometimes people have to pay extra for empty properties.