What Burbank said.
Think about it this way: the top is the part of the guitar that's actually getting driven by the strings. Sure, they push on the neck some, too, but the neck is so stiff and heavy that it's not going to move nearly as much as the top. We make the top light, and _just_ stiff enough, so that it can move as much as possible, and produce sound.
The sound comes off both surfaces of the top: inside and outside the guitar. If the box were not enclosed the sound from the two surfaces would tend to cancel out, since the air could just sneak around the edges and fill in, instead of making noise. A guitar with no sides would probably have lousy efficiency, like a piano.
Some of the air vibration inside the box is communicated to the outside world via the soundhole. One function of the hole is to introduce a phase delay so that the sound coming off the top and out of the hole will be in phase at some pitch. We call this the 'main top' resonant mode, often around the open G string pitch.
About an octave down from that is what we call the 'main air' mode, where the sound coming out of the hole and the sound coming off the top are out of phase. If the top is the only wood part that's moving the two will tend to cancel out at that pitch, just like the situation you get with no box at all. _Any_ movement of the back and sides at that pitch will tend to give a net flow through the hole, and some sound production at the low end. So, the main benefit of a flexible back is probably in the low end response. Guitars with light, flexible backs tend to have a lot of low-end 'punch' because the back can really get into the act down there.
But when you come down to it, the back isn't nearly as good a 'loudspeaker' as the top. It usually weighs more than the top, for one thing, so a given amount of energy put into the back will get you a smaller amplitude of vibration that you would get from the top. Besides, it's pointed in the wrong direction: toward your gut, rather than the audience's ears.
On the plus side, that added weight means the back can be a good 'flywheel' once it gets going, storing sound energy and feeding it back into the air and body. Most of the prefered back woods have really low damping, so thay can ring for a long time.
Still, once you get past the 'main back' resonant mode, most of its resonances are losers, stealing sound from the top and wasting it. All of the higher order modes have more than one vibrating area, after all, and those tend to cancel each other out.
If you look at the output of a guitar that's been driven with some sort of a signal that has the same amount of energy at all frequencies, you'll see that most of the back resonant pitches show up as dips in the spectrum. It turns out that's not all bad. It's the pattern of peaks and dips in the spectrum at higher frequencies that seems to make the sound 'interesting'. You'd prefer to make peaks, by getting the top to be more active, but 'the back we will always have with us', and if a few dips make it sound better, what the heck. Ovations don't have any back resonances to speak of, so there's a reference to the ultimate 'stiff' back sound. You just don't want too many dips in the spectrum, nor do you want them to be too spread out in frequency. That's another good reason to use a back material that 'rings' nicely when tapped: the low losses make those back resonances have narrow bandwidths, so they only steal energy from the top at certain pitches.
As always, there's no one 'best' way to get a 'good' sound out of a guitar, just a lot of good ways. Light backs and heavy backs can both work if you get the rest of the instrument to do what you want. And, as always, I'll say that the whole thing is probably a lot more complicated in detail, so that there will be times when this sort of simple explanation falls down. It keeps things interesting.
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