According to the diagram included with original
Notice to Trainmen issued for the resignalling in 1972, these were labelled as carriage siding so presumably they were intended to store stock between services or incoming holiday trains. The now removed second siding shown on the diagram was also connected at the other end so locos could run round in the siding if needed. How often this loop was used when loco hauled trained were the norm, I've no idea.
I'm not sure, but I'd imagine it would be a very long time ago. As access to the siding is controlled via a ground frame which is released by an Annetts Key locked from Bristol Panel, so post privatisation it would likely need someone from Network Rail/Railtrack to come down from Bristol to operate it. As the years went by, the risk of stabling a train on a siding that that hadn't any usage or maintenance for years would increase making such use more unattractive to operators. At the moment, there's currently a Stop board on the siding track just beyond Drove Road bridge, presumably because of the poor state of the track.
The reason it doesn't appear on the maps is probably because it's not controlled directly by Bristol panel, all they can do is remotely release and lock the Annetts Key located in a cabinet by the ground frame. That said, the crossover at Yatton is on the signalling maps which is also controlled by ground frame with Annetts Key, so it may just be more to do with excluding unnecessary detail in a station area.
You're underestimating how busy Weston-super-Mare is. There's the hourly Cardiff-Taunton/Exeter, hourly Severn Beach/Avonmouth terminator plus the 2-hourly London Paddington terminator which waits in the station for 50 minutes. There are additional London Paddington services during the peak and the 1 tpd XC in each direction. During the day, there's a train somewhere on the loop 80% of the time on average. During late running, it's not unusual for services to have to wait on the main line because both platforms at Weston are occupied. This in turn delays the non-stopping CrossCountry services which are timed to pass Weston on the main line between the local trains.
It would certainly be a very useful to put the Severn Beach terminator in there when the Paddington terminator is also in the station. However, I suspect there's next to zero chance of it happening before the line getting redoubled, which itself won't happen until money is found to replace Hutton Moor Road and Locking Moor Road bridges on the loop.
PS to OP, it's a lower case "s" in super, i.e. Weston-super-Mare. The "super" means "on top of", as in superficial or supervisor, hence the lower case.