There are a few ships where this would be nice - mostly small, highly mobile ships with omni shields, where I really want to be piloting in strafe mode, but still need to angle shields to, say, not take a salamander up the engines. Wolf and Omen in particular; the latter is almost uncontrollable without strafe mode, and has wide-angle turrets that you want to aim, and - with accelerated & extended shields - is quite good enough at not taking damage when on full autopilot.
The other place this would be nice is actually the Paragon - and that's not so much shields as it is ship system. On full autopilot, it's extremely good at "pulsing" fortress shields - taking reduced damage from most hits, without reducing its outgoing firepower by any notable margin. I can't do that under manual control. So, there are times & opponents, where it's actually better for me to put the ship on autopilot once I've manually flown it to more or less the right place.