This is a question that perplexes would-be sound engineers the world over. It is fairly common knowledge that if you drive a loudspeaker too hard, it will blow. Therefore it seems sensible to err on the side of caution. But you have to know exactly how manufacturers decide on the rating for a loudspeaker. You know what? There is no precise measurement they can do. So they guess. Yes, they guess!
Guessing right is important. Build a speaker and stick a 50 watt rating on it, and you may suffer from your competition who are saying that their loudspeakers of the same size and price can handle 100 watts. Guess too high and your users will be blowing your cones to the other side of the room. So a manufacturer has to give a loudspeaker a rating that looks impressive, but doesn't risk too many instances of blowing, leading to a bad reputation.
If as an engineer you choose to err on the side of caution and drive a 100 watt full range loudspeaker from a 50 watt amplifier, then you might feel that you can push the fader as high as you like without concern. However, of that 100 watts of which the loudspeaker claims to be able to handle, maybe 6 or 7 watts are normally sent by the crossover to the tweeter. If you push your tiny amp too hard, it will clip (distort) and generate massive levels of HF. So your small amp can indeed blow your big, beefy speaker. Well the tweeter anyway.
An experienced sound engineer would far prefer to have a big amplifier to hand, and then control the level carefully. It's like having a big engine with power to spare, yet being gentle on the throttle. An experienced engineer will listen carefully to the sound the loudspeaker is producing. If it sounds stressed, he or she will simply back off.
In conclusion, a larger amplifier is generally better, but needs careful handling. Smaller amplifiers are no safer.
By the way, if a manufacturer wants to put a really high power rating on his loudspeaker, all he has to do is design it so it is inefficient. Most of that power will then dissipate as heat rather than sound!
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