It's just easier to quickly notice a pattern moving or standing still than the needle moving by a few degrees. The needle can also appear twitchy or jump around and lag, making it harder to tune accurately.

Pitch detection is computed and can sometimes be influenced by external noise or sampling limitations.It can jump. However, the visual display is based on the period of the reference note (or set frequency), allowing it to function independently of the detected pitch.

I guess this is a similar idea to the Peterson Strobe tuner? I think they have a rotating object which presents dark and light regions at the chosen frequency, which is a similar idea to building a visualisation on a set of samples whose length is the period of the chosen frequency.

Same basic idea, like an untriggered oscilloscope tuned to a fixed frequency/period.

This is a great answer. If I understood correctly: The feedback you give the user is different than a usual tuner in two ways: it is framed by the reference note, and is two-dimensional.

Yes. The pitch displayed and needle interface is based on measured frequency. It also shows the nearest note name based on this measured value. The visual waveform interface's stability is based on reference frequency set. There is still scope for improvements to detect the pitch variation of plucked strings and provide an analysis. The tuner supports Just intonation which are based on ratios. Here fundamental, fifth and octave have perfect ratios (1, 3/2, and 2) and they can be visualized. Kindly try if you have an Android mobile. There is also a play button to sound the reference note.