My woofers at home are 15" and the speakers are flat to 20Hz. I never have problems with the woofers flopping about. But I am careful to make sure the cartridge isn’t too compliant for the mass of the arm. If it is, as the cartridge negotiates the minor ups and downs of the LP surface, the mass of the arm will take more time to catch up with the cartridge. This causes a lot of low frequency output from the cartridge and its stuff that isn’t on the LP surface.
You can either reduce the mass of the tonearm or decrease the compliance of the cartridge. The former might be done by replacing hardware holding the cartridge in place (or going with a lighter cartridge); the latter is done by replacing the cartridge.
Is this part of the logic behind the Dynavector dv507 arm having a pivot configuration which minimizes vertical moving mass?
Isolation issues can also greatly impact woofer flapping. I had occasional problems when I was using a poor Lovan rack (stackable modules, not very rigid). They completely went away with an upgrade to CMS Maxxum - still using the same kind of table, speakers, cartridge, arm, amps, same positioning, etc.
15" Tannoy drivers here so when the woofers flap at all it is VERY easy to see. Floor here is suspended wood, but old world commercial construction - not nearly as compliant as modern residential suspended floors. Still not like a concrete slab either, though.