Nice post.
I have periodically done this type of exercise for years.
First influenced by Virgil Donati on his instructional video Power Drumming focus on one hand moving one note subdivision around the kit hitting every sound source.
Next by Steve Smith on his instructional from back in the day, Steve Smith 1, where this two-handed flow of note would be practiced over a bass drum ostinato (repeated pattern).
Last influence to this type of exercise was after seeing Jojo Mayer in clinic 2-3 years ago where he suggest starting with 8th notes at a slow tempo with no accents or fills for at least 5mins. Striving for:
consistent even tone between the hands,
accuracy in timing,
volume balance and personal mixing of the kit,
melodic phrasing around the kit
This is great for fundamental fluent movement about the kit and solo endurance. However, one has to to limit it's usage because you can get caught up soloing cause other weaknesses in ones playing.