Great question!
No the owner is not being insensitive. It was a rental that the owner owned.
First, If they keep it vacant, then all the other tenants will have to deal with looking at a death apartment with the traffic of people trying to come in and look at the place. That would be really insensitive to Heath's memory and to the tenants that currently live in the building.
Second, they really shouldn't have to keep the place vacant and keep paying to maintain the place. The owner shouldn't be running a place at a loss, or they might have financial and emotional trouble as well.
Third, after he passed away, who do you think had to pay to clean the place up after everything, including the original stuff, the police and general traffic going through, etc. This will continue on if the owner keeps it vacant.
Fourth, the price is really high. Some might debate that, but it keeps copycats out of the place for the most part.
I have no idea who owns the place. Anyone interested in finding out, should go and find out who the building is registered to, and if it is a business, to find the registration information. You should be able to do this easily if you live in New York City.