I don't know. Tilt-shift may be great for correcting the perspective distortion of tall buildings but on landscapes, it makes them look so unnatural and/or diminishes the "grandness" of such sights are a high waterfall or a deep canyon. Or maybe it's just me.
"Shift" corrects for "falling over backwards" from tall buildings and gives them a more natural look. Sometimes you DO want to have the falling-over since it's kind of a photojournalistic approach. But the shift lens tends to be a one trick pony and I found that I didn't have much use for my Nikkor 35mm shift lens.
But "Tilt" is a whole new kettle of fish. It's primary function is to make the depth of field take a new angle. Briefly, the D of F from every camera you've ever used is a plane that's parallell with the back of the camera. So anything in front of, or behind this plane of "in focus", will be blurred. We can use the aperture to increase this D of F but only to a point.
With tilt we take that plane of depth of field and "lay it down". For example you tilt the lens down and the D of F follows the plane of the front of the lens (more or less). Subsequently you get the foreground in focus, at the same time that the background is in focus and often with a large aperture.
Imagine that you are in an alpine meadow and want to get flowers in the foreground to be sharp, along with the mountains in the background, and f22 won't do it. If you were to look at a sideways drawing of this example you'd have a horizontal line with you and your camera standing at one end. In front of the camera would be the flowers and then further along the line would be the mountains. You tilt the lens down and adjust it back and forth until the new plane of D of F cover the flowers and the mountains.
It's easy enough to do. You just keep an eye in your viewfinder and play with the amount of tilt until it looks good since "The groundglass is truth".
This is all view camera technique and a very useful tool. Sideways tilt is called "Swing" and is used to change the plane of D of F from being foreground to infinity, to left to right. Say you are standing next to a brick wall which is on your left. You want the bricks to be sharp in focus and once again aperture alone won't do it. You focus about a third of the way down the wall and see that the foreground and background are soft. You then "swing the lens" left and the whole wall will come into focus.
There is no distortive effect of using tilt or swing on the image. In fact you see shots every day (commercial table top food shots, for example) that would use some type of lens movements.
"There's never time to do it right. But there's always time to do it over."
Canon 5D, 50D; 16-35 f2.8L, 24-105 f4L IS, 50 f1.4, 100 f2.8 Macro, 70-200 f2.8L, 300mm f2.8L IS.