In the 1960’s the most popular subwoofer being mated with the QUAD ESL was the 24" Hartley. The rationale for the use of a larger woofer cone is not to produce more bass, but cleaner bass.
A 24" woofer cone does not have to move as far as does an 18" to produce a given SPL, one benefit being the woofer’s voice coil will therefore better stay within the magnet’s maximum field strength. Lower excursion results in less distortion. The same for an 18" vs. a 15", a 15" vs. a 12", etc. Of course that presumes all else is equal, which is not necessarily the case.
Rythmik Audio offers subs with woofer cones of 12, 15, and 18 inches. They are all servo-feedback controlled, and sound more alike than different (except for the utterly unique OB/Dipole Sub, each of which contains two 12" servo-woofers mounted in an open baffle frame. It is VERY different from sealed and ported subs).