You may always connect those subplots through events. A possible solution is given in this Stackoverflow answer of mine: Using Matplotlib 3D axes, how to drag two axes at once?

from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
import matplotlib.pyplot as plt
import numpy as np

n_angles = 36
n_radii = 8

radii = np.linspace(0.125, 1.0, n_radii)
angles = np.linspace(0, 2*np.pi, n_angles, endpoint=False)
angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1)

x = np.append(0, (radii*np.cos(angles)).flatten())
y = np.append(0, (radii*np.sin(angles)).flatten())
z = np.sin(-x*y)

fig = plt.figure( figsize=(13,6))
fig.subplots_adjust(left=0, right=1, top=1, bottom=0, wspace=0)
ax = fig.add_subplot(1, 2, 1, projection='3d')
ax2 = fig.add_subplot(1, 2, 2, projection='3d')

ax.plot_trisurf(x, y, z, cmap=cm.jet, linewidth=0.2)
ax2.plot_trisurf(x, y, z, cmap=cm.viridis, linewidth=0.5)

def on_move(event):
    if event.inaxes == ax:
        if ax.button_pressed in ax._rotate_btn:
            ax2.view_init(elev=ax.elev, azim=ax.azim)
        elif ax.button_pressed in ax._zoom_btn:
            ax2.set_xlim3d(ax.get_xlim3d())
            ax2.set_ylim3d(ax.get_ylim3d())
            ax2.set_zlim3d(ax.get_zlim3d())
    elif event.inaxes == ax2:
        if ax2.button_pressed in ax2._rotate_btn:
            ax.view_init(elev=ax2.elev, azim=ax2.azim)
        elif ax2.button_pressed in ax2._zoom_btn:
            ax.set_xlim3d(ax2.get_xlim3d())
            ax.set_ylim3d(ax2.get_ylim3d())
            ax.set_zlim3d(ax2.get_zlim3d())
    else:
        return
    fig.canvas.draw_idle()

c1 = fig.canvas.mpl_connect('motion_notify_event', on_move)

plt.show()

I guess one could easily extent this functionality to any amount of axes, but I currently wouldn't know where in the code to put that. As a figure level method? Or a new class? Using a Grouper object?

fwiw I feel like a recipe such as the one you proposed is good enough...

The problem with this recipe above is that it uses the "private" _rotate_btn and _zoom_btn. I'm personally not very stringent about using such attributes, but I guess if proposing this as some "official strategy" (e.g. as example on the matplotlib site) people wouldn't like it.

I think this would be a nice new feature - kind of like sharex and sharey, but for 3D plots.

Yep, just mind that rotation is a priori independent on sharing. You might synchronize the viewing angle, but not share the axes or vice versa. This is easily accounted for when manually creating the callback, but for some automated option it will require two independent groupers or similar.
Not saying this shouldn't be implemented, but I suppose there are much more important features in the mplot3d category to fix/implement first.

cc @nfoti

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Attn @scottshambaugh ?