Without trying to come up with numbers, I'm gonna go out on a limb and just claim that typical instruments accurate enough to keep you on an IFR route are probably not accurate enough for guiding a pilot down a runway of whatever width for very long.
I’ll jump in here and say they are. Gyros are analog instruments. All you’re looking at is the DG.
Why emphasize analog? If you can see well enough to focus on the top of the Instrument, ANY movement from where it was when the aircraft was centered is visible. A tick mark of movement is too much.
The old jokes about flying within half a needle’s width applies.
Now... is the pilot good enough to STOP the movement. That is the real question.
Examples one can try without a CFI aboard are making an altimeter needle stay absolutely glued to a mark on a smooth day. Off your altitude by 50? How about shooting for 10? How about a wiggle? How about not allowing it to move?
The Instrument isn’t the weak link. The eyeballs and skill set of the person looking at the Instrument are.
Most of us can handle it in a car too. Can you keep a needle glued to a speed better than your car’s “autopilot”/cruise control? Sure you can. Especially if you have a tachometer. It multiplies by speed.
I say this about analog because SOME digital stuff is too granular to do stuff like that. As long as the resolution and fractions of data points are small enough, digital can mimic analog. And delay in processing can also be a factor on old stuff.
Analog gyro? The gyro is rigid in space and it thinks the world is turning around it. The Instrument shows tiny tiny changes you probably can’t correct accurately for. But you can learn to average your corrections. And it takes heavy concentration.
The heavy concentration part is likely where this went all wrong. A distraction could be disastrous. That’s the risk analysis one has to remember trying to concentrate hard enough to be that precise. Other instruments have to suffer being mostly ignored for a very short period of time and if something divides your attention, you may be screwed.