It's difficult to do splits at an intermediate station as crew would have to ensure there were no passengers in the unit that's going to the sidings. This would probably be done by locking that unit out at St Pancras, but then there could be delays at the intermediate stations (potentially impacting on the critical timings of Thameslink) as people try to board the locked-out part.
A common strategy for peak strengthening is for alternate workings at the end of the peak to be run to sidings as full-length trains, with the others then being split in the platform to form the next two return journeys (and the reverse at the start of the evening peak). This uses half as many ECS paths and drivers as splitting/joining each working individually, but does need extra platform space because the train that splits will still be in the station when the next one arrives. Hence it wouldn't work at Corby where ECS paths would be possible to/from Kettering, but there is only one platform. It might not work at St Pancras either as the platforms will be fairly heavily used and ECS paths to/from Cricklewood are more difficult. The other problem is that it doesn't work for reducing 12-car to 8-car, and a three-way version of the same idea to split down to 4-car would need even more platform capacity.
So all in all I agree with Failed Unit that there are likely to be a lot of 12-car units in the off-peak periods.