With enough practice, most sight pictures can be learned, so long as your eyesight is healthy, and you repeat the activity A LOT.
Not my shooting, but here is a recent 1.41moa 10 shot group from 200m, using a No4-223 + rear peep sight. A No4 fractory blade, with a gehmann 530-579-0 rear peep for astigmatism correction:

- No4 223 + Gehmann 530-579-0
- 356448375_974530413690391_2270897704596804233_n.jpg (203.72 KiB) Viewed 1016 times
And here is a double-bagged group from my No4-223 + central-No4:

- No4 223 + Central No4
- thumbnail_IMG_1321.png (418.19 KiB) Viewed 1016 times
So yar. As you can see, irons can be shot almost as well as scopes... so long as the sight picture is repeatable, as is your cycle.
About the trigger, again, pretty much any trigger can be learned. If you observe what happens on a digital trainer, a heavy two stage service trigger will often jump off to the right at the moment it breaks, but this is ok ... so long as you repeat this technique, from hundreds or thousands of repetitions. Dry fire is key.