I think it would be silly for Stewart to do a "Neil Peart" Style drum solo, and I don't think he would want to do one anyway.
His rhythmic talents are best used in support of a song. If he was doing a personal composition that was primarily percussion oriented, I could see that as being sort of a solo....but that would be out of place for most Police fans.
Andy's soloing is pushing it a bit much on this tour, but that is probably because Sting wants to use this tour to "highlight" Andy and Stewart to make up for all his attention grabbing 25 years ago. Either that or he is just lazy and let's Andy go forever so he can rest his voice.