This is a subject that gets debated until the cows come home!
The suggestion of it being a good idea to have a more powerful amplifier than speakers is because of "head room".
For example, a 300w rms speaker can usually handle short term peaks of 4 times its RMS rating i.e. 1200w
A 300w amplifier cannot supply enough watts to cleanly provide power for any transient peaks up to the 1200w. According to the Crown link, an amplifiers RMS and peak power are nearly the same. At best it will allow 1db for peaks but transient peaks can be up to 25db or more.
It is therefore recommended that a more powerful amp is used to have some power in reserve (headroom) for the transient peaks.
Using a more powerful amp doesn't mean that it will be any louder. For example, if the speakers are 300w RMS and a 600w amp is used, the volume should be at the same level as it would be if you used a 300w amp. The extra 300w is the "head room".
The problem is:
1) Most DJ's have no way of knowing how much power they are pumping into the speakers and are likely to pump more than 300w rms into them
2) If the power is there, there is a temptation to use it.
3) If you clip the amp, drop a mic or get feedback with a 600w amp connected, you are more likely to damage the speakers because of the extra power.
As it says on the Crown site quote"If you cant keep the power amp from clipping (say, you have no limiter and the system is overdriven or goes into feedback)
the amplifier power should equal the speakers continuous power rating"
So basically you should only use a more powerful amp if you have a limiter and you can be careful enough not to push more power than the speaker RMS power rating in to it.
Using the Enquirers analogy, if the engine is represented by the amp and the rest of the vehicle is the speakers:
A 300w amp with 300w speakers is like the the 2CV that will do 90mph
A 600w amp with 300w speakers is like the 2CV fitted with a Ferrari engine, i.e. it is still only safe to do 90mph in it because the transmission, suspension, tyres, brakes, bodywork etc won't cope with anymore but the ride will be a little less stressful
A 600w amp with 600w speakers is like the Ferrari and will happily cruise at 125mph
It is also interesting that active speaker manufacturers such as Mackie match amp and speakers. The transducer (main speaker) in a Mackie SRM450 is 300w RMS and the amplifier powering it is 300w RMS. So if its good enough for one of the worlds top selling speakers, its good enough for me