There is such a high turnover of staff at many London garages it is probably not worthwhile to teach newcomers all the routes only for them to leave again.
Some drivers prefer a bit of variety whilst some are happy to be on the same route day in day out.
I can certainly think of an example in London where a driver will stick to one bus route: the W10, which is just a single-bus operation and will on weekdays generally be found with a friendly driver called Sam behind the wheel, as immortalised here. (Before that, it was a chap call Paul.) I think they like it as they get to know the regulars on what is a very quiet bus route. I have in fact sometimes wondered whether the drivers have the facility to ask to drive just one particular route or if in fact they drive it day-in-day-out simply because that's what they've been told to do.