It depends on the turn. With training you can do gentle turns (std rate, 15° bank) with the artificial horizon, turn coordinator, and watching the compass. When doing standard rate turns I watch the nose on the horizon, the turn coordinator, the compass, and the vertical airspeed indicator.

Once you get into 45° and 60° banks the forces are disorienting and it's far easier to look out the window at the ground and the real horizon.

Training or not, it's far easier to look out the window to make turns. You can see if the horizon is starting to move. If you sit there and watch the compass you can easily enter a stall or a dive without realizing it. Especially since your turns are not going to be coordinated (you won't be using the rudder effectively so the forces on your head will not be what you're used to).

Compass is one of the most complicated instruments to master in the aircraft because it behaves differently depending on many factors: where you are, where you turn, and are you going up or down:

https://en.wikipedia.org/wiki/Aircraft_compass_turns

However if you do, then you have a backup instrument that never fails.

Compass lags, trying to keep a heading via the heading indicator is trickery than it sounds. Ground references are the way to go.

I won't get into how inaccurate a compass can be in a plane because I understand your meaning - we can turn a plane accurately using instruments. But keep in mind that the first step is to learn how to fly visually using ground references.

Not really, because by looking outside you would also control the angle and atitude instinctively, you could do it using the compass too, but if you are flying visual you better be looking outside.