NPCs can't handle people who can fly, FA off has nothing to do with it.
A few cases in point...
[video=youtube;g22IXU57NYo]https://www.youtube.com/watch?v=g22IXU57NYo[/video]
[video=youtube;9gPWWnpf5Ak]https://www.youtube.com/watch?v=9gPWWnpf5Ak[/video]
In the first video, I destroy a deadly NPC corvette for an elite rank standard assassination mission with a very general purpose courier, and never take a single hit.
In the second, an Engineered FDL and vultures (during a wing assassination) struggle to cope with my own corvette, flow aggressively.
NPCs have certainly improved over time, but there are still major gaps in their piloting. They won't use FA off, even when it's wise to, and they can be prompted into repetitive, disadvantageous, behaviors if one can approach them correctly.
I've successfully completed a couple or three FA Off landings (including with rotation correction off) and while they were satisfying to achieve, I found them too much hard work to do every time I land somewhere. But I don't know if I'm gimping myself by using a XBO controller (which, by itself is pretty good to be fair) as opposed to HOTAS or KB&M.
While I don't have access to a HOTAS (actually I tell a lie, a friend has one but it's pretty worn so doubt it'll yield any precise sense control) I never really tried KB&M. Might give it a go and see if it provides more nuanced control if anything. Although the idea of using a pointing device to simulate a stick is putting me off all the same.
Edit - just to clarify, as opposed to the OP I'm not that interested in PvP performance, more about the different maneuvers you can pull (such as flying horizontally across a planet surface while cockpit facing down etc.).
I imagine it's mostly an issue of finding bindings appropreate to your controls and becoming proficient with them. Personally, I favor a decent HOTAS setup, but there are enough excellent pad and KBM users to convince me that the inherent advantages/disadvantages of most quality controls are relatively minor.
As for flying over planet surfaces, this is actually one of the areas that FA Off provides clear cut advantage. With good thruster acceleration to gravity ratio, you can certainly fly in any orientation over a planet with FA On, but if you are too far off horizontal, you have to constantly fight the thrusters...and if gravity is high or thrusters weak, the increased demand on them will melt the ship. FA Off removes all of that and you additionally gain the ability to peg the ship at full boost velocity almost continually with a minor gravity assist.