Not the cycle path - the benefit of that being a sensible width is obvious. The segregating build-out bit.
I'm not sure of the actual reason, but it seems to me that something thick enough for a pedestrian to be able to stand on it while waiting to cross is desirable. 'Pedestrian' might reasonably include a wheelchair or pushchair, though hopefully there are dropped kerbs at proper crossings for those.
Given experiences of Magic Paint, I'd say that more than a brick's worth of physical space between the motor traffic and the cycle path users is also desirable.
But also, it may function as a tactical reduction in road with, in order to reduce motor vehicle speeds. Sometimes that's appropriate, but I can't speak for this location.