Because there was nothing to gain and everything to lose. Leningrad was a very large city, with a huge industrial capacity (someone of which, unbelievably, continued to be used during the siege). It didn't make sense to give it up at least in the event that the siege would eventually be lifted. It was also an important port on the Baltic, the last remaining in Soviet hands. Giving it up would have let the Germans to supply their troops more easily. Lastly, Leningrad remained a priority target for the Germans, and they kept a significant number of troops in the area. Once Leningrad fell, the Germans could have used those troops elsewhere, like Moscow or Stalingrad.

As far as the humanitarian reasons go, there are good reasons to believe that Hitler would not have been generous with the survivors of the siege. In fact there was a plan to completely eliminate Leningrad from existence.