If I were planning a journey, I would want the actual elapsed duration to be shown from the time I board the first leg to the time I alight from the last leg, so if there is a 9 minute wait for a leg involved, I would expect that to be included.
There is a little known trap involved with duration though. It only affects high frequency periods of operation for bus services as far as I know, not low frequency or rail/tube services of any frequency.
If you specify a journey on a route which runs every 10 minutes, the duration presented to the passenger is the time on bus plus the 10 minute interval between buses. It is not at all obvious that this is being done. At least it is not obvious until the high frequency daytime service changes to low frequency evening service, at which point two successive buses arrive at your destination at roughly the same time!
One consequence is that any sensible passenger will already be factoring in some waiting time, so will get an inflated and off-putting impression of how long it would take. If you want to make a journey using three high frequency services it will add half an hour on!
Another consequence can be observed by looking for buses form Enfield Town to Chase Farm Hospital, with three alternatives which leave from three stops in different roads. Two are low frequency, one is not. During the day Journey Planner usually advises using one of the low frequency services because adding in the interval for the high frequency service appears to make it arrive later! Illogical, captain! In reality, the high frequency service is the best best unless a low frequency bus is almost due.
It has clearly been set up this way by design but the logic completely escapes me.