Taxes add to the cost of a unit and thus end up adding to the price of a enit. So in a market like NYC you'd be pushing up the price of these units. AS for having these wealthy people pay less in taxes if they "reside" in a unit goes, how exactly are you going to police that policy? How exactly are you going to determine who is staying in a resident without violating some basic rights of property owners and the right to privacy, etc.
Uhmm , I don't know how to say this other than to tell you that you have no idea what you're talking about. An increase in taxes does not increase the cost of the unit for residents of NYC. Period. Also, an increase in taxes in absolutely no rational way would make the property more lucrative as you previously claimed. It would only make it more expensive for those not living in it, which is the whole point.
If your argument is that they will increase their sales prices to compensate for the taxes in time that will make their prices uncompetitive with other sales. The market corrects that easily.
As for verifying if the owner is a resident, that's super easy. You apply the assessment to the owner of each property unless they filed NYS taxes as an NYC resident with that as their address. If they aren't a resident there's no way they will fake being one on their tax return to avoid the assessment (as NYS tax rates are almost certain to cost these high income individuals more).
That should cover it all.