I think the Class 56s on stone trains still needed banking to Warminster - without a banker the max load would have been ~12 of the typical 100 ton wagons used on the Mendip flows.
I remember seeing 56s come through Salisbury on ARC stone trains in the late 1980s (alongside Yeoman 59s which would not have needed a banker).
For example this is a photo of 56041 being banked by 56056 in 1987, with a typical consist of 16 or 17 wagons (I think this might be the lunchtime 7O83 Whatley - Fareham):
https://www.flickr.com/photos/74384955@N03/7263963870/
Searching for "Salisbury Class 56" on flickr brings back the memories! I suspect banking would have become much less common once the ARC Class 59s were introduced in 1990/1991, displacing the 56s on these workings.
With the current traction types in use today, assuming ~100 ton fully loaded wagons, a class 66 is authorised to haul (roughly) 17 loaded wagons, a 66/6 maybe 18 wagons, and a class 59 can haul 20 wagons up the gradient to Warminster without assistance. The stone terminals served on this route (such as Fareham, Botley, Eastleigh, Woking, Southampton) are in many cases limited by train length as much as weight, so there wouldn't be much advantage to banking the trains these days anyway.
However, I found an interesting (fairly) recent case of banking assistance to Warminster...
This photo shows 66034 on a Merehead - Eastleigh working at Westbury Yard in 2016, substituting for the usual class 59:
https://www.flickr.com/photos/dbs60100/24181494889/in/photostream/
It's part of a sequence of shots showing it being banked from Westbury Yard up to Warminster, with the assisting loco detaching and using the crossover to return to Westbury (click the right arrow to see the other photos).
In general, if a 66 substitutes for a 60 or a 59, the load (number of wagons) would be reduced accordingly, if necessary. However, in this case it looks like the train ran from Merehead to Westbury with a load intended for a 59. It would have been fine between Merehead and Westbury, but then would have been too heavy for the route from Westbury to Eastleigh. Rather than leaving 2 or 3 wagons at Westbury, there was obviously a loco and driver available to bank it, maybe to repeat the nostalgia of former years! So while banking is not normally done, it appears to still be possible in terms of the signalling and crossover at Warminster.
I think this is because "Westbury Yard" in TOPS is traditionally a single location covering the up and down yards, but the current Network Rail planning systems are more specific. Some trains show departing from "Westbury Up Reception" but there are others (such as weekend possession trains) that will usually show departing from the Down yard regardless of which yard (up or down) they are starting from. Within the TRUST system itself, a departure that shows as "Westbury Down TC" on RTT will actually appear as from "WESTBURYY" i.e. from Westbury Yard rather than specifically from the Down Yard. However, the underlying planning systems (linked to the data feeds that RTT use) define this location as "WESTBURY DOWN T.C."
Location names that appear on typical enquires within TRUST are limited to 9 characters, so for example Birmingham New Street shows as BHAMNEWST. This is fine for an internal system where people are used to the abbreviations required to fit the character limit, but for the public data feeds the fuller description makes more sense and gives more information.