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.

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.

Not all planers have poor bass. My Apogees have plenty of bass, but it is different bass than a cone speaker. It is tight and defined and tuneful and goes deep, but it just doesn't have that hit you in the chest slam of a good cone woofer.

Why do planars have poor bass extension?
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Sideshowgabe

maybe because you've never heard a good planar setup?? I'm with Ptmconsulting on this matter - my bass is fast, tight, tuneful & goes as low as the room will support (about 40Hz) but it does not sound like a cone woofer boom-boom-boom bass.
2nd reason you could be disillusioned with planar bass is that planar bass sounds different from cone boom-boom-boom bass which is the only thing that 99% of the people know. So, when you hear planar bass, you ask 'where's the bass?' It's all in there just that it does not call attention to itself like most cone woofers do.