I'm a bit skeptical that adding reset kwarg may be too ad-hoc and won't carry us through all clear-related issues ( #28851). While it may be a route to make clear() behavior configurable, are we sure there are only to variants, so that a bool parameter is sufficient?

You write

When 'reset' is set to False, part of the formatting of the axis (labels and relative properties) is left unchanged.

That's too imprecise. We need to be very clear what is changed and what not.

The naming "reset" is quite generic. Have you thoroughly reflected whether this is the best name?

Is there a reason to use **kwargs? If possible, explict parameters with a default should be preferred.

Agree with @timhoffm that this is not the correct approach here. Multiple meanings of "clear" are just going to get confusing and there will always be the question of where to draw the line of what gets cleared and what does not.

Thanks for your feedback @timhoffm and @jklymak

You're right that this is not the solution for all the problems cited in #28851 as well as that in this case an explicit parameter with a default value would be preferred being the "reset" parameter always used in the function.

Then how do we want to treat this PR? Do we want to proceed as suggested by @jklymak and as said here #28268 (comment)?
In this case this PR would close the only problems related to the labels position (that was my initial target here), leaving the other topics unsolved for now (e.g., resetting axis scale of child plot when clearing the parent one or not resetting tick label).

IMHO it is a good idea to proceed with @jklymak solution since it won't create too much confusion, but it would also be a good enhancement to make clear() behaviour more customizable (not using just a bool parameter like my "reset" but something more explanatory that could accept multiple values as you said)

That's my first PR so pardon me if it is not perfect :)

@dberardi99 Thanks for taking a crack at this - your contribution is appreciated. Given how mature Matplotlib is, making changes to basic functionality like ax.clear is going to need a fair bit of thought and discussion.