max lenz, the most important reason in favour of doing it your way, (way ‘A’ – clearing all waypoints before the FAF), is that in the event of a go around, you’ll have LNAV and VNAV available to look after the (perhaps complicated) missed approach.
If you’re under radar vectors, you may not (probably won’t) pass within the necessary distance of these waypoints to have the FMS clear them from your active plan. If you have to go around, you’re stuck with steam-driven lateral and vertical navigation until you clean the flight plan up – a potentially distracting process in a what can be a very busy time of flight.
Engaging L and/or VNAV without first taking the time to clean the flight plan up (or after making a mistake in cleaning it up) could turn the whole shootin’ match into a real dog’s breakfast. If you engage LNAV, the aircraft will want to head straight for the first bypassed waypoint after you went on to radar vectors – probably behind you. Selecting VNAV in such circumstances could give you any number of nasty surprises.
On an approach, crosschecking by the non-flying pilot should be done from raw data sources, not the FMC.