Alas, that would be a terribly idea, because all of a sudden you have the government snooping into your living arrangements. Especially for grey areas where people share their time between multiple apartments. Way too complicated.
And, people living in bigger places would get effectively get a discount this way.
Your argument does highlight a problem with the transition phase of the introduction of the tax, though. There's a few ways to solve this, eg by slowly phasing the tax in over a decade or more.
(It's not a problem in the long run, because land prices will drop until the financial burden of tax plus mortgage payment is the same as today.)