In the sound reinforcement world, the 1.5-2x amp power: speaker power handling ratio is often used, because owing to the dynamic nature of music, average power to a speaker is much less than peak and speakers can indeed handle transient peaks well in excess of their rated power handling. Using a power amp rated for more power than the speaker it's driving allows a bit more transient headroom before amplifier clipping. This is perfectly reasonable and commonly done. It does mean you need to be judicious with how you operate things, though, because if you're running heavily compressed program material or the system limiters are clamping down hard, you clearly do run the risk of overpowering the drivers to the point of damage.![]()
If you put more power in to a speaker than it can handle mechanically, or thermally, you will damage the speaker. There is no minimum required power to effectively run a speaker. One may prefer the tone of an amp pushed to a certain point, or the tone of a speaker as it goes in to nonlinearity, but those are not requirements.

. For those following along 1 db is considered the minimum a human can discern, 3db is about what one would call "significant" - a doubling of the power.