The discussion would be a bit long. I believe it is useful, at the beginning, at least until the appendix to Ciriaco's first course, or even until the completion of the first course, to clearly explain the subdivision. It is even necessary to make one understand and internalize the double subdivision. Naturally, in solfeggio performance and musical performance, the subdivision and the double subdivision must not be highlighted by gesture or accent, but only internalized and thought of when necessary. Naturally, I am only summarizing things that for many teachers and others are obvious.
Take the first page of Beethoven's Pathetique op. 13 and perform this exercise also on the double subdivision (the sixteenth note) and we will obtain the maximum precision in the division of the beats and the figures that represent them.
It is also obvious that the fragmentation of accents, i.e., their highlighting, increases with the slowing down of the tempo. In a grave, a greater number of small appoggiaturas are expected, and then some subdivisions become strong... even within a weak beat. Moving towards Adagio, allegretto, allegro tempos, the accentuations decrease until they only take into consideration the accent of the strong beats or even that of the beginning of the measure. A classic example is a 3/4 that in a Presto tempo is conducted in 1. Opp., exceptionally, do not be scandalized, a very slow 6/8 which is better to conduct in 6.
Naturally, regarding the solfeggio course, it is a cause for reproach at the exam to see a student who "subdivides," but rhythmic precision and naturalness in reading difficult rhythmic cells are highly appreciated, perhaps deeply understood (using the visualization of subdivisions) and "once and for all and without uncertainty" during study sessions with one's own Maestro.
P.S. a fundamental lesson is the one dedicated to the differences between simple meters and compound meters. Even today, I sometimes notice a lack of absolute clarity between the two "different natures."