Sorry, but there are many false and misleading statements in ssscientist's post! This MUST be addressed!!!!
As with all such sweeping bromides, the answer is a qualified 'yes'. It is true that if you attempt to run underpowered speakers for long periods of time they will 'blow' or in technical terms 'sustain damage'.
You can run underpowered speakers forever without them "blowing" or "sustaining damage". Provided that you never clip the input of the amp. Even if you clipped the input of the amp, they MIGHT still survive. There is no "given" that they will blow just because they are underpowered, just that they are more LIKELY to blow because you are possibly clipping the input of the amp.
And no, you can't pump a kajillion watts into computer speakers and expect them to do anything but smoke.
You can pump a gajillionkajillion POTENTIONAL watts into computer speakers and they would be fine provided that you never actually USED the full wattage. If the input level to the amp was low enough, the output potential would never be realized.
Same is true for 100 watt amp driving 30 watt speakers. When making a purchase try to get both the amp and the speakers to match as closely as possible. 30 watt speakers can only get so loud, and overpowering them is not going to make them louder.
I probably wouldn't go over by that amount, but it wouldn't scare me to do so if I found a great deal on a 100 watt amp to drive my 30 watt speakers. The rule of thumb is to match the amps potential output by 1.5-2 times that of the speakers Peak power handling rating. THAT is what creates "headroom".
A higher quality amp will deliver much better results than a lower quality amp as far as headroom, frequency response, lack of transient smearing, etc.
A high quality 20 watt amp trying to power 100 watt speakers lacks headroom just as much as a low quality 20 watt amp trying to power 100 watt speakers. Headroom has everything to do with the amount of power you have above what you NEED then anything to do with the relative quality of the amp. Also, almost every amp I have seen made in the last 30 years will deliver the usable frequency range for human hearing. In fact, I have used quite CHEAP ass amplifiers that deliver everything just fine. If the amp can't deliver 20hz - 20khz then something is quite wrong with the amp that needs to be fixed. Now, if you want to get into class D power amp talk and stupid stuff like that, I suppose you can defend your argument, but I don't see many people trying to use a car stereo sub amp to power studio monitors, nor have ever heard of anybody asking about doing that!
On the flip side, 1000 watts of low quality power will not do anything for your monitoring system except cause problems.
Define "low quality power" please. Certainly, few studio monitoring systems need this much power, but again, depending upon the speaker used, it may fit PERFECTLY. I keep thinking of the old UREI monitors with the double 15" woofers and horn. Easily, they can handle 500 watts each speaker! So, I guess I am not feeling your statement here because it is sort of empty of a point.