Possibly on the grounds that
Tuesday am: there isn't good reason to get a load of passengers to London who can't be guaranteed a means of getting home. For instance, what happens if you take a few trainloads of people from Uckfield to London and they all turn up at Tunbridge Wells later in the day hoping to get the 29 bus home?
Wednesday pm: As I understand it the strike affects shifts with booking on times up to 10:59 so therefore it is unlikely sufficient guards are back at work to operate the Wednesday pm service in time.
It's not so much about the booking on times for the evening shift. Traditional "late" turn (evening peak related) conductor shifts at Southern start way after 1059, and there are relatively very, very few "middle" turns, perhaps excluding Link 1 Barnham, and Redhill. In theory there should be very few issues getting crew to book on for the afternoon & evening peak due to a strike which ends at 1059. However, the likelihood is of a major risk to the network caused by going from a relatively "cold start" to full functionality - will mean contingency resources will be stretched to the limit to move stock to the right places for the evening shift to pick up their trains. Stock diagrams will be severely affected, and therefore there will be many handovers mid-journey booked for the start of the late turn which will simply not happen due to the trains themselves being in the wrong places. Running a simpler service on Wednesday evening means that resources can simply be allocated to a clockface timetable, to pick up trains as and when available.
As an example, starting the Uckfield service from scratch on a gradual basis as the late turn book on could be a recipe for disaster. London Bridge - Uckfield is a relatively complex route due to the traction used, specialist route knowledge needed (for example, various shunts needed for service) and suchlike, over which relatively few managers and assessors will therefore be trained. This, by the way, is not speculation. As such you can only really rely on competent Selhurst Conductors and a couple of other staff to work the route. Seeing as most of those conductors will probably be on strike in the morning, the stock may be in any number of inaccessible sidings at Selhurst and elsewhere by mid-afternoon when the late turn book on. The diagrams would need heavy amendment to avoid these trains being relieved on their journeys based on the usual stock and crew diagrams starting in the morning peak. Many such diagrams involve a web of crew changes across the whole route, not just East Croydon; you may be missing a train at London Bridge, a driver at Norwood, a conductor at Oxted and so on. Now multiply this by all of the other routes Southern do, all the varying stock and route knowledge, and all of the innovative methods needed to berth a large amount of stock during disruption.
So it's not just about booking-on times on Wednesday; in fact, if anything, that's the easy bit!
