I think you have a point. And of course all his adult kids with have Secret Service protection as well. It'll be very expensive, and given they travel all over the world for work, will be even more expensive than usual. But it's been our tradition for a long time.
What hasn't been our tradition is presidents as insensitive as Trump is. In his place, most would realize that spending a lot of time in New York would be a very considerable expense, and also a very considerable inconvenience for New Yorkers. Usually, when presidents have had a second residence--like, for example, Bush's ranch--they haven't been in cities, and security was relatively easy. During Obama's first term, he and his family went back to visit their Chicago home a few times, but apparently they found it just wast worth the trouble to themselves and their neighbors. Evidently The Donald doesn't give a shit who he annoys, or how much it costs.
But the question of the First Spouse is different. Melania may not have a good reason for her apparently lack of interest in playing the role, but she won't be the first. We will have a woman president one day, and if her husband isn't of retirement age or older, I doubt he'll want to quit whatever job he has to do ceremonial stuff at the White House. The same will no doubt be true for many wives. Jill Biden was in a way a precursor: she continued to teach full time while she served as Second Lady, if that's a title.
Perhaps it's time to redefine the First Spouse role. As things are now, it's a full-time unpaid job. And that's wrong, really. It's no longer relevant to our culture.