All are equally dispensable, but I think the true answer to your question is "none are"
Theoretically, any rotation in 1 direction can be created from a series of rotations in the other 2.
- to yaw 90 degrees left in a spacecraft with no yaw control, you can pitch up 90 degrees, roll 90 digress right, and then pitch down.
- to pitch up in a spacecraft with no pitch control, you can yaw left, roll left, yaw right, and then roll right.
- to roll, you can pitch, yaw, pitch, and yaw.
My Quaternion-fu is not perfect, but with the loss of any one of the primary 3 axes leaving only 4 functional thrusters, in 2 pairs, both at 90 degrees to each other, you should be able to perform any possible re-orientation in no more than 16 applications of thrust on the remaining thrusters. (8 rotations = 16 thrusts. As each rotation needs two thrusts, and all thrusts need to be in pairs as you need to start pitching up and stop pitching up in two separate applications of thrust.)
This limitation means you're unable to track a target along certain axes. If your enemies spacecraft is lacking yaw control, then you should manoeuvre to their left or right such that their main guns are unable to track you as effectively.
You're also going to be disorientated while yawing in a craft which lacks yaw control, as you'll be pitching and rolling all over the place to arrive at your target orientation. While your disorientated, you'll be vulnerable to attack.
This reorientation is difficult to perform manually without giving it your full attention, if you're in battle and need to track this complex manoeuvre is going to be easy to make a mistake and end up lost. If you need to change your target orientation mid manoeuvre (eg tracking a target heading in that unavailable rotation) you're unlikely to be able to do that without a computer.
All the thrusts in a manoeuvre need to be strongly ordered - you must wait for your pitch comes to a complete stop before applying roll, otherwise you'll end up with residual yaw at the end of your manoeuvre, this will further complicate tracking. If you had all 6 thrusters, then you could overlap thrust inputs if required for a much faster turn.
In open space, these limitations are equal for all 3 primary rotation directions.
There are multiple frame challenges to your assumptions here:
You can use a gyroscope to reorient your space craft, this requires no propellant and no external thrusters to reorient your craft. It's turning circles will be quite large though, so it'll be unable to achieve tight WW2-like dog-fights. But a craft with only 4 orientation thrusters will also make for some pretty boring dogfights too.
Thrusters need not be complex things that would need to be reduced to simplify design, they're amoung the simplest systems on modern spacecraft. You can make thrusters with only a single valve (I.e. a single solenoid) and no other moving parts, which requires only a single digital output from your flight control system (on / off), amplified through a single transistor. Hydrazine can be sprayed onto a strip of an Iridium catalyst which ignites the hydrazine and expands out a fixed nozzle, generating thrust.