Is this correct to say?
You cannot do the same corrections that the shift functionality does (e.g. make vertical lines of a building you photographed from ground level straight again) in PP because un-distorting it in PP will treat all pixels the same regardless of what the distance from the camera was. But objects at different distance need different correction.
Consider two buildings, one smaller one in front of a bigger one. With shift you can get both building's verticals straight, in PP you would do the wrong correction to one of them when one is correct.
Of course you could do multiple PP steps and cut things together. And usually you only care about one thing at one distance.

