I've used RTA analysis of a 1KHz sine wave on an LP. Some LPs have single channel tracks.
I examine the ratio of the off channel 1KHz signal to the in channel 1KHz signal. I perform this on both channels. Once I meet specs, I usually stop. Sometimes this leaves an imbalance in the off channel minima. If the values are both less than the spec for the cartridge, I consider azimuth optimized.
One can argue that I am not aligning the stylus. This may be be true. I won't argue. However, the method I use always produces extremely low distortion (<0.25%) with excellent channel balance.
Visual alignment is very subjective, even with a mirror or some other mechanical tool. The resolution of the eyes of most people is not good enough to accurately set the stylus azimuth. This statement comes from years of doing visual alignment.
Of course, all the other stylus/tonearm/turntable adjustments and alignments must also be optimized in order to obtain the results I achieve.

