I can see at least two reasons behind this subtlety of expression.
1 It gives the R&F membership a veneer of scholastic integrity. Upto 1950, when the first edition of the NWT of the "Christian Greek Scriptures" was published, the general expression was the "New World" when referring to the post-A structure of society. Then Freddy Franz the "oracle" of God discovered an anomaly.
There are two Greek words used in the NT to discuss a concept such as this: "Kosmos" which he decided to "translate" as "world", and "Aion" which he tabbed with the expression "system of things" Now he found that when references to the Post-A time were made in the NT, the word used was "aion" not "kosmos" [check out Lu 18:30 etc] So Voila! Out went the expression "New World" and say hellow to "New System"
The ironic bit was that Franz discovered this anomaly too late. The New "World" Translation had already been published. So there we were like a bunch of gits, prattling on about the "New System" while at the same time flogging the New "World" Translation at the doors.
2 It keeps the faithful on their toes. Blues Brother will bear me out in this, but back in the 60s and 70s you had to keep on your toes to show that you were up with the latest '' truths'' and this meant remembering all the subtle shifts in verbal nuances. If some unfortunate specimen, in a lapse of judgment at an otherwise boring WT study, mentioned the word "world" when he should have said "system" you can bet your boots that he would be stared at like he was a skunk at a family picnic. And that would be the only bit that was remembered at the study. Such peer tactics ensured he never repeated such a clanger.
BTW, I remember about the late 70s the WTS making quite a hullabaloo over the word "Armageddon" insisting on printing it as "Har-Mageddon" This caught the more zealous ones off guard. Could'nt tell if it was a one-off thing or a new "Shift" in vocabulary.
With many of their best writers either pushed out or voluntarily leaving, and with a dearth of deep theological thinkers left behind, this verbal rectitude seems to have blurred, and guards, both theological and linguistic, have dropped.
In other word, no body gives a stuff.
Cheers