Why is the position of the pilots' head (eyes) so important?
The correct seating position is important to ensure

A consistent viewpoint, which results in the final approach and flare always looking the same to the pilot. This is important when hand-flying the aircraft to ensure consistent landings.

Having a consistent viewpoint gives several operational advantages such as easing the handling of the aircraft by providing pilots with a consistent visual reference, repeatable at every flight. This is especially useful during final approach to be familiarized with the final approach path angle and also for the flare phase.


Best forward visibility, which maximizes the area in front of the aircraft you can see (Visual Segment):

Having the seat further backwards or lower would reduce the Visual Segment.

Good View of the Instruments, which allows seeing the PFD and ND without having to move your head down. This is how it looks with the correct seating position:

And this is how it looks if you are seated too high or too far forwards:



All sources: Airbus - Are You Properly Seated?

You also asked

Can't a pilot tell if they see enough, above/below/on each side, by just looking?

Yes, not all aircraft have the three balls for finding the optimum seat position. You can do it by looking over the glareshield and ensuring good visibility of the PFD/ND. On Boeing aircraft, this is how it is supposed to be done since they don't have a dedicated eye reference indicator:

Pilot Seat Adjustment
Adjust the seat position with the appropriate controls to obtain the optimum eye
reference position. Use the handhold above the forward window to assist. The
following sight references are used:

Sight along the upper surface of the glareshield with a small amount of
the airplane nose structure visible (A)
Sight over the control column (in the neutral position) until the bottom
edge of the outboard display unit is visible (B).



(Boeing 737 NG FCOMv2 - 1.40.44 Airplane General - System Description)