Why do planars have poor bass extension?

I think you're right -- the diaphragm's tension limits its excursion so that it can't move enough air to generate adequate volume at lower frequencies.

Solutions seem to include bigger panels to move more air and augmenting lower frequency response with dynamic woofers. In the latter case, driver integration is a significant challenge, since the panels tend to be very fast while the dynamic woofers can be slow.

The 20.7 (and the prior 20.1) has a magnet structure on both front and back of the diaphram to improve bass performance and slam. (lesser models have the structure on only one surface)
The main reason for lesser bass performance is the fact it is a dipole. The bass from the rear meets the bass from the front at the sides and self cancels a lot of the bass.
Any full dipole is gong to have the same issue. That is why you see so many with a cone woofer stuck on a dipole.

One trick is to add 'wings' to the sides and the bass gets better, as it has more distance to go to self cancel at the sides.
I use a 6" panel addition on my Magnepan 3.6s just off the bass side (none on the tweeter side)

Also the panels flex, and the various stiffening stands also improve the bass response.

I've read accounts that make sense to me that often the support structure is the weak link in the bass of planars. The frames tend to not be very massive and there is little inertial foundation for the drivers to work against. Adding mass and/or rigidity to the frame helps. At least that's what I've read that seems to make sense.

Also, many do not realize that most planars like Magnepan forexample require lots of power (though not necessarily current) to be driven to the max. A 40-80 watt SS amp might sound OK, but does not hit the mark. 200W+ SS or a larger tube amp is usually what is needed to wake things up.