That’s a common way of handling it. A non-FAA “part 1 PIC” column in which you log time actually in command, excluding some time the FAA permits to be logged as PIC and including time the FAA does not authorize to be logged as PIC.
Where you get into a thicket is what time “properly” goes into it. That varies. I’ve heard the same arguments about that for about two decades. Safety pilot PIC is a good example but there are others.
“The airlines don’t want your time in the right seat of a Cessna 152” (an opinion on what an airline thinks of it)
vs
“safety pilot PIC time is Part 1 command time” (an accurate regulatory statement).
My thought on the subject is simple. What you put in your logbook is data entry. From a regulatory standpoint, that data entry is the subject of 61.51 (and cross country logging rules). What else you put in is up to you so long as your totals for FAA purposes meet regulatory requirements
[edit] and the FAA can tell the difference from looking at it in a logbook review.
What you put into an application is a report using on a query based on what the application asks for.