We were told that the tables were based on 10m/min until the first stop (perhaps it was 9m or 12m, I don't quite remember since I wont be doing deco dives and subscribe to Sherlock Holmes' theory about remembering useless stuff), otherwise we ran the risk of on-gassing too much for the table to be completely valid.
Given that nearly everyone is using a computer these days (at least for the kind of light backgas deco included in the 3* syllabus), and the computer tracks any ongassing during a "too slow" ascent, I assume that it was an exercise in following a predetermined ascent strategy rather than a real deco exercise.
The 88 tables solve the problem of variation in ascent rate by defining a dive as the time from leaving the surface to reaching the ascent check depth (6m on a no stop dive). So if you ascend really slowly, then your 'dive time' is longer, potentially moving you to a new surfacing code (or potentially compulsory decompression).
Now when I was teaching ERD, and Bhulmann tables (which are used by BSAC for Trimix courses, and ERD before it was dropped). The ascent speed is critical, if diving to table, rather than computer.