They weren't used for take off because there was no relevant mode. The initial climb was to hold 250kts after takeoff until a predetermined time for noise abatement (a little over a minute ex-LHR, less ex-JFK) and then start to accelerate after the NA thrust reduction.
It was a balancing act and different for each departure - the RoC actually went up the faster you went so you were easing up, maximising the acceleration, while ensuring you (just) made the SID alt requirements.
So, apart from a few seconds holding 250kts, there really wasn't a mode that would work in pitch; you would have to take vert speed and be constantly asking the NHP to select different VS's and HDGs and they had quite enough to do already. No benefit, so don't use it.
Once you'd got to Vmo during the SID (it was 400kts at that point) you could use Max Climb mode (see earlier discussions) and that was generally when the FD was engaged.
It was permissable to engage the AP at an early stage, in which case HDG mode and Pitch Hold would be used, but it was more effort than hand-flying, less accurate and less fun so that was a rare event.
On approach, if an ILS was being flown, you are correct that the FD could be used, although for a typical approach it needed to be off at 300'. This was because wherever possible we flew a 'Reduced Noise Approach' (again, see earlier comments) which consisted of holding 190kts to 800' then reducing to final speed to be stable by 300'. AP/FD had to out by 300' in this case, owing to the very tight pitch control required for which it wasn't certificated (although it could carry out a very good coupled approach and landing if given a more stable approach).
In summary - a very 'hands-on' aeroplane. And all the better for it
