Obviously we may be constrained by backcompat, but it is not clear to me why we'd expect cla() to reset the scales, but not the formatters and locators?

Notice that this is in the context of a shared axis, say the x-axis being shared between Axes A and B. You start by making A, setting its scale, locators, and formatters. Then you make B, sharing it with A. This calls B.cla(). What the code is doing is making B.xaxis.major refer to A.xaxis.major; these are Ticker instances, which are just references to a locator and a formatter (and the same for .minor). So this is the somewhat indirect and obscure way that the sharing of locators and formatters is done (contrary to a comment in the tickers module that locator instances should not be shared, if I remember correctly).
Next, before my PR, all the shared locators and formatters are copied.
Then the scale of the new B x-axis is set to match that of the A x-axis, using a call that also sets the shared locators and formatters to their defaults, even if they were changed on A from their defaults.
To fix that error, they are all restored from the saved copies.
In this PR I just eliminate the saving, the resetting to defaults, and the restoring.

But the short answer to your question is that in this context, with a shared axis, cla is not resetting the scale, it is just setting it to match that of the axes with which it is shared.

Now, this works correctly on initialization of B, but I just did a little test, calling B.cla() after plotting in A and B, and, with 2.0.2, it did not do the right thing--it preserved the x scale (which I had changed to log), but it reset the locator and formatter to the linear defaults. I think this is a bug, perhaps related to the earlier unconditional call to self.xaxis.cla() in B.cla().

OK, I understand your explanation.
Do you plan to address the later bug that you mention in this PR as well? Otherwise I think this can go in.

@anntzer I would prefer to have this PR go in as-is; I think it provides a little bit of cleanup with no side-effects (unless I am missing something), and is only peripherally related to the bug. I have been digging in to the sharing and aspect ratio business a bit, and the bug is just one part of that. I'm not sure whether it will make sense to fix it independently, or as part of a larger set of changes. I suspect the latter.