I think most of the answers have been already given as to why (it relates to the old way of calculating gun data manually), but the key one being you only have to order it out once at the start of the fire mission. It is correcting not only for non standard conditions, but also for the position of individual guns as it relates to Bty centre. The former is determined prior to fire missions, based on the setup (or battle) range for a given charge, and the latter is determined for each relevant fire mission and based on range to target from Bty centre
But as to specific ref's, a general description of fuze correction is in B-GL-306-006 AP-001, Field Artillery Vol 6, Ballistics and Ammunition (in particular Chpt 6, Sect 4, Para 23, but there is also other relevant info in that tome)
It should also be in the ref for instruments that includes the Manual Artillery Plotting System (that's a controlled document so I can't tell you its name etc)
The old TFT's for the M109, the AM2, also gave a very detailed explanation of why for all arguments of entry and gun data calculation. The last time I seen a TFT for the Cdn M777 that information was not in there. So you might have to go digging around in the unit library to see if they have an old copy of that M109 TFT (which, IMO, does a far better job of explaining manual data calculation than what I've seen come out of the School)