On that note--let me run an idea by everyone:
What would you say to the possibility that the Section 31 of the 24th century is not
the 31 of the 23rd century--and the latter is not
the 31 of the 22nd century?
By that I mean that Section 31, having "overreached" and made a significant amount of screwups, is regularly "taken down" (say, by the Kirk Cabal or SI)--and "re-built" by new faces, or lower-ranking agents who escaped the purge. After a short period of being underground, in which it re-grows...it effectively restarts.