Yeah, loudspeakers are one helluva system, lots of aspects interacting. Alright, lets make a thought process
Usually the box is for a woofer to prevent sound from back and front of the cone to cancel, better efficiency for bass. Now think a box for bass for now, simplified. Take some bass woofer and model a box for it, lets not get any deeper than this. Perhaps you took 6" driver or 15" driver or anything that was familiar to you. Now, either of them will require very different size box although they could play pretty much the same wavelengths only at very different sensitivity as the other one would have more cone area.
Alright, two different drivers, two different size boxes, two different circumstances for problems to appear even though the application is pretty much the same, play some bass and have enclosure to play it efficiently not losing it in destructive interference. Common thing for both is wavelength of the bass they are supposed to play. Both are smaller than wavelength for the very low bass and at some frequency the box is half wavelength in size and internal standing waves happen which add some to the soup.
Alright, when wavelength is much longer than the size of the box what happens inside the box? Pressure changes pretty much uniformly inside. What are implications of the pressure change to the box walls? They balloon some. As there is a lot more surface area on the walls than on the radiator this might be significant (audible) if you allow them to. The ballooning depends on the pressure of course but also things like stiffness, joints on the corners, what frequencies the box (walls) resonates as the resonances would be the most audible, easily excited and would ring longer than the excitationg signal. Bracing to rescue. Bracing and other techniques are to make the box panels resonances higher up in frequency, out of bandwidth of your bass box. You could also dampen the resonances which is easier when they are higher up.
Problems arise when a bass box also plays midrange like in two way speakers, it might be impossible or at least hard to push resonances past the pass band to many kilo Hertz, especially the case with a big 15" box, much harder than with small 6" box. In this case it could be better to split the band in two, have separate bass box who is stiff not to resonate on passband and another box for the mid who then could even be a floppy one! Have resonances below the pass band. Or just use damping to kill high frequency resonances. Or have no box at all for mids because it doesn't play bass
Vast subject.
Hows that turned into practice? For bass box, any bracing is good, extensive is just more work and at some point diminishing returns, use at least one between each opposing walls. You might use math or accelerometers or someone elses work to get some hunch what the panel resonances are and how much bracing is actually needed to shift them. You could also check out what makes the resonances where to put braces in order to have less braces more effective. Braces might also harm (at least do no good, only change things) if the box resonances were below pass band but now pushed up to the pass band.
Some people go crazy with it while some seem to be more pragmatic. For example mr. Geddes uses single brace for all opposing walls, so total three, tied together on the middle with shear damping included, its big two way box and cast from some material so a different case than subwoofer made from MDF or small shoebox.
