Well yeah, x is specifically the thing you control, y is the thing you don't. For all but the most trivial systems, y will be influenced by something besides x which will be a source of noise no matter how accurately you measure. Noise in x is purely due to setup error. If your x noise was greater than your y noise, you generally wouldn't bother taking the measurement in the first place.
“ If your x noise was greater than your y noise, you generally wouldn't bother taking the measurement in the first place.”
Why not? You could still do inference in this case.