Here are the view angles I would propose. This matches matlab's conventions and keeps the roll angle at 0. The inverse views show the other 3 sides of the box, and are defined by a 180 deg rotation about the local vertical axis. Might be worth a PR at some point to make all the axes in these orientations show along the bottom and left edges. (Edit: see #23644)

import matplotlib.pyplot as plt

# (view, (elev, azim, roll))
views = [( 'XY', (90, -90, 0)), 
         ( 'XZ', (0, -90, 0)),  
         ( 'YZ', (0, 0, 0)), 
         ('-XY', (-90, 90, 0)), 
         ('-XZ', (0, 90, 0)),
         ('-YZ', (0, 180, 0)), 
        ]

fig, axs = plt.subplots(2, 3, subplot_kw={'projection': '3d'})
for i, ax in enumerate([ax for ax_row in axs for ax in ax_row]):
    ax.set_xlabel('x')
    ax.set_ylabel('y')
    ax.set_zlabel('z')
    ax.set_title(views[i][0])
    ax.set_proj_type('ortho')
    ax.view_init(elev=views[i][1][0], azim=views[i][1][1], roll=views[i][1][2])

This requires adding a right-click menu in a backend independent way? I think that will be a huge benefit in general as well, being a right-click person...

Yeah, I see the scope of this as twofold.

1. Programmatic interface to look at primary view planes. I think DOC: view_init docstring for 3d axes primary view angles #23600 is good enough to suffice this, but maybe we accept "XY", etc. strings as an input to view_init as well.

2. Right-click context menu to expose this to the gui. That's a pretty big chunk of work I'd expect.