More than likely is down to operational convenience, it may be possible after huge sums of money are thrown at the problem, but it would be difficult enough without COVID.
I saw mention of Waterloo and 375s. That was in no way the same. A small pool of driver managers and high grade driver learnt the two miles or so from Voltaire junction/international flyover to Waterloo international for a service lasted several days.
Best case scenario would be the 707s were left at Clapham Yard, South Eastern would have to learn from Clapham yard (SWR), round Latchmere and come out at Wandsworth Road, plus a full traction course. The alternative would be SWR drivers learning from Clapham Yard the whole way to SE’s depot.