Adding sidelights to a front entrance that does not have them
A door is held up by hinges in the jamb (the broad boards surrounding the door, perpendicular to the surface of the wall). The jamb is thin material, usually a little over 1/2 inch thick, but it is firmly nailed to the jack stud, which gives it rigidity, as does any casing added between the jamb and the wall. The header also sits on the jack stud.

While you might theoretically be able to move the king studs to the outside of the sidelights, you cannot move the jack studs outward. This would render the jamb the total support of the door (unacceptable) and would extend the span of the header (undesirable, often requiring a deeper header). 

Also the king studs, which tie the king/jamb/door structure into the bottom and top plates would be further apart, reducing the rigidity of the structure nearest the door, where most of any flex occurs. Finally, any molding joining the jamb to the sidelights would likely be much narrower than traditional casing, again reducing rigidity.

Unless there is a compelling reason to narrow the vertical spacing between the door and sidelight, go with full stud/sidelight/king/jack/door ...

Even if there were a compelling reason, engineers and inspectors might disagree.

An exception might be for a sidelight/door/sidelight structure designed as a unit.