Since there are crossovers at City Hall and Raffles Place from EWL to NSL, I feel that SMRT should provide direct service form EWL to NSL and vice versa. The service can be alternate, which means,
"Your attention please, the oncoming train at platform A will crossover to the North South Line to proceed towards Jurong East via Woodlands after City Hall Interchange. Passengers going beyond City Hall on the East West Line, please wait for the next train at platform A.".
"Your attention please, the oncoming train at Platform B will cross over to the East West Line and then proceed towards Pasir Ris. Passengers going to Marina Bay, please wait for the next train.".
This can help to ease congestion at interchange stations as well as ease congestion on EWL trains after it picks up passengers from NSL.
Plausible when u consider the fact thattrains used to run from YCK to Outram Park. But for the sake of planning and to ensure trains don't collide, they would rather separate it. If trains were to cross over from Tg Pagar into northward direction, then how about trains coming from Marina Bay? There may be problems with train bunching, thereby posing a safety hazard. Similarly, if trains were to enter the west or east branch from NS25/NS26, trains may have to slow down in anticipation of the train ahead. So there will have to be a bigger gap in between trains just for trains to come in from NSL/EWL, hence translating into longer wait.
The one plausible manner to carry out your solution is to create an additional trrack so trains can come in safely to suck in / dispose passengers at either stations. Something like NS1 / EW24 Jurong East