Yes, a lot of HF will blow out your tweeters. No question. But the bass end? Well there are a couple of things to say about this. Firstly, although some power amps most certainly can pass DC, it's a seriously bad idea to pass it to the speakers. For a start, there's not a room around that can reproduce frequencies anywhere near that low, and any small DC offset in the amp output will cause a permanent deflection (although this is usually pretty small) in the resting position of the cone. So AC coupled speakers are a good idea, because with DC coupled ones, the slightest fault will take out the speaker cones, and even if you have switch-on transient supression, this won't protect your speakers from the inevitable damage that an amp fault will cause.
But the biggie, and the one that seems to be most misunderstood, is the power handling one. Let's just consider first what happens when an amplifier clips at a level below the speaker power handling limit - the under-powered amp situation. The speaker cone has mass, which means that it takes time to accelerate. When your amp output clips, the cone will continue to travel in the direction that it was going, even though it's not supposed to. Not only that, but it generates what's known as a 'back emf' in the form of an error signal, which will actually be reflected in the amp's output. What happens at this point varies rather, according to what type of amp you've got, but it ain't good, and it sounds dreadful, however you look at it. But the real problem is that it's actually not too good for the voice coil. Coil wants to stop, cone is going to keep travelling... Pretty soon, as they try to part company, this will loosen the windings, and this is when you get 'grating' noises from your speaker.
So what about the other way around? Plenty of output from the amp, which isn't going to clip yetawhile. And the speaker cone suspension will hit the end stops, where it will promptly make a horrible clicking noise that you really won't like. But with modern-day speakers, you have to do this for quite a while before damage actually starts - unless of course you overdrive so severely that you rip the cone straight out of the speaker. Yes, the voice coil will warm up, and eventually burn out, which is another good reason for not continuing this for too long. But believe it or not, this is actually less likely to damage your speaker than the underpowered situation will.
And it will sound better, too. If you run an amp up to its clipping point, it's going to produce far more distortion during the peaks than a relatively underdriven but more powerful amp will. So the general rule is (if you want to play safe, and have good sound) that if you've got 50W rated speakers, run them off a 100W amp, and use a bit of common sense about the levels.
So, you run your underpowered amp into clipping a lot of the time, thinking that your much more powerful speakers will handle it okay, and actually, they're not handling it very well at all!
