The Queen also bought Andrew that monstrosity he and Sarah had built - dubbed South Fork which was recently torn down by the new owner. So the Queen tried to set Andrew up as she had Anne & he did pocket the $13 million or so from its' sale. Andrew's 75 year lease for Royal Lodge at Windsor was arranged after he vacated the property the Queen originally gifted him. So there's precedent for the monarch to gift their children real property.
Edward seems to be the child who received the least, a 50 year lease on Bagshot.
In regards to Harry's finances, I'd submit that he has not traveled to as many exotic locales for weddings & vacations as his cousin Beatrice has in the last couple of years and like her he has his trust from the Queen mother. He also has the money he inherited from his mother. The income from his investments more than likely adequately covers his private activities w/out any need to dip into his capital. He may opt to acquire real estate, or he may opt to inhabit whatever residences the family offer him.
When William and Catherine were considering apartments at KP they supposedly looked at Princess Diana's place and at Princess Margaret's and chose the latter, so I assume the former could be made available for Harry. There are 3 sets of elderly Royal cousins w/ KP apartments/homes that will become available at some point in the future - the Michaels, Kents and Gloucesters, although perhaps not soon enough to fit Harry's needs