This is a two part issue:

1. The documentation was wrong Revert invalid change in Centered Ticklabels example #13578.

2. Even when setting the alignment for each tick individually, you won't get what you are expecting. The alignment takes place with respect to a reference point. Therefore

import matplotlib.pyplot as plt
import numpy as np
import matplotlib as mpl
print("Matplitlib version: %s" % mpl.__version__)
 
x = np.logspace(-2,3)
y = 1 / (np.exp(1/x) - 1)

fig = plt.figure(1, figsize=(4, 4))
plt.loglog(x,y)
plt.xlabel('x')
plt.ylabel('y')
plt.tight_layout()

ax = plt.gca()

for label in ax.yaxis.get_ticklabels():
    label.set_horizontalalignment('left')

will result in

Ok, thanks a lot.

@1
Well, this is of course a perfectly valid answer :) Unless I am mistaken, the page that I linked to still lists this solution as valid?

@2
Ok, thanks. While I realize that this is maybe not the ideal place to state this, I think that adding alignment of ticks is a worthwhile addition to matplotlib.

If anyone knows a hotfix, I'd be happy to know.

@1
You've linked the docs of the current stable release. They will only get updated on the next release. The current development docs are here https://matplotlib.org/devdocs/gallery/ticks_and_spines/centered_ticklabels.html

@2
May be a bit tricky because the alignment would have to be a common operation depending on the size of all other labels. Until now the parameters are just handed through to each label. This would probably need an internal 2-pass approach (e.g. if fontsize is given simultaneously, that would have to be applied first to determine how wide the labels are and have to be moved.).

As a workaround, you can do

ax.yaxis.set_tick_params(pad=32)

or if you don't want to tune with hard-coded numbers

width = max(label.get_window_extent(fig.canvas.renderer).width for label in ax.yaxis.get_ticklabels())
ax.yaxis.set_tick_params(pad=width+2)

Labeling as hard (borderline wontfix, I'd say) because making all y labels talk to each other to achieve proper left-alignment would require quite a bit of work, I think.

This might be handled best via a TextCollection class as proposed in #4063.

@timhoffm it seems like the issue has been fixed with 3.3.1

I think the docs have been fixed from 3.1.1 (looking at the milestone on that PR), but I think that @timhoffm suggestion to render the figure once to get the text sizes and then shift the padding out is the only reliable way to do this currently.

This issue has been marked "inactive" because it has been 365 days since the last comment. If this issue is still present in recent Matplotlib releases, or the feature request is still wanted, please leave a comment and this label will be removed. If there are no updates in another 30 days, this issue will be automatically closed, but you are free to re-open or create a new issue if needed. We value issue reports, and this procedure is meant to help us resurface and prioritize issues that have not been addressed yet, not make them disappear. Thanks for your help!

The docs are fixed and even though it is annoying, the behavior from #13440 (comment) for setting the left alignment is the correct and expected behavior. You can adjust the pad on the tick labels to push them out.

If you are willing to use axisartist this is supported:
https://matplotlib.org/stable/gallery/axisartist/demo_ticklabel_alignment.html

I am going to close this as resolved.