Summary

Inspired by #31392 (review)

Should we constrain the public API?

In particular, I don't think set_locs is needed publically. Calling format_ticks(values) should be sufficent and it should be possible to make the locs state an implementation detail.

Additionally, one could check / clarify the relation of __call__ and format_data. Are both needed publically?

Also #5804 may be considered.

Proposed fix

This is a tracking item for the idea. It's not yet ready to be worked on, because we first need a deeper analysis on the current usage and a discussion on the desired API.