Looking at the pics you’ve posted, and comparing the two example local routes using Google maps, you’re right that the through-estate route potentially saves the cyclist a couple of hundred metres on a route where passing under Wandsworth Bridge makes sense.
However, the decision has evidently been made to strongly favour the pedestrian and amenity for local residents through the estate (the planters, 5mph speed limit etc), and encourage cyclists passing through the area to keep to the main roads. It is accessible to local cyclists (who’s actually going to enforce that dismount?), but if you want to ride briskly, you’ll stay on the road.
Which seems reasonable. If separatist infrastructure for cyclists is ever a good idea, it should be carved from space currently dominated by the motorist, not poor old sods tottering off for their pensions, and kids playing outside.