Can a power amp have too much power, risking damage to a speaker?

A general rule of thumb we see in service of loudspeakers 

too much power sent to a speaker cooks woofers (from being too loud, beyond the dynamics of the speaker)

underpowered usually cooks tweeters as the amp runs out of power and begins clipping ( clipped output = square waves = impossible for a speaker to follow a square wave precisely so it overheats trying to )

Brad

@phillyb

From the number of damaged speakers we get in for service, I dont think your idea works in practice. And Im lost when you say "know when a recording comes into its own at a particualr power level". I assume you mean that you should be able to hear when it begins to distort? Gosh I wish you were right becasue if this were true I would never get a blown speaker/driver in for service!

I’m also not clear on this idea that Recordings have a favored or preferred power level (assume you mean playback SPL). Playback systems systems do have a maximum power level, but Im not sure they have a preferred or even minimum playback SPL we could all agree on.  QUADS were notorius for having a very limited max power level and limited dynamic range so perhaps your hearing is oriented around this?  (Billy Woodman from ATC loved loved loved quads for their extreme definition).

Recording systems also have "preferred" input gain settings as well but even this is up for debate in practice. There is a well known story of the Beatles arguing with the Abbey Road Engineers that a distorted input signal (exceeding the preferred input gain of the system) was NOT a mistake.