Probably.
To fit a lift in that could hold two people, the top would likely have to be much wider than it is already.
Which would be a lot more material in building the tower.
And while I don't know the science behind these towers, I imagine there's a perfectly good reason why they are thin at the top.
Also, you'd need space for the lift mechanism at the top, and the top would have to take the strain of pulling up the lift. And as the top is the smallest part, it's weaker too.
And if there was a malfunction with the lift at the top, it would probably be much much more difficult to get people up to fix it.
Or the elevator maintains an absolute size all the way to the top instead of completely conforming to the towers dimensions and there would be a catawalk that extends from the elevator to the location in need of repairs. No need to worry about lift malfunctions. As stated the tower already has a lift so if it malfunctions there's someone out there already who can fix it.
So really its none of those things, it would just be really expensive like we agreed upon.
