This is a proposition to deprecate logistic_regression_path and make it private.

Context: #11476 (comment)

Making it private would make it much easier to refactor the code in LogisticRegression and especially in LogisticRegerssionCV, where a lot of case-by-case logic has to be implemented due to non-homogeneous array shapes.

The deprecation should not affect users. Quoting a mail from @amueller who has looked for occurences of the use of logistic_regression_path on GitHub repositories:

Can confirm it's not used anywhere. I get 12 hits in the 46081 files using sklearn,
all of which are vendoring scikit-learn as a whole (so it's not actually used).
For comparison, LogisticRegression is included in 3980 files (many duplicates and forks of tensorflow)
and in 1662 projects (identified by project name, which is likely underestimating, since not all projects named "kaggle" correspond to the same project).