Why do speakers improve with more powerful amps?

Lots of overthinking on this subject but usually, common sense goes a long way. When I purchased my KEF R3 speakers, I had a conversation with a KEF engineer about suitable amps and he pointed me to a blog on their website about power requirements. At its most basic level, choose an amp that is 60 to 110% of the recommended power requirements if published by the speaker manufacturer. Ignore the minimum number because it is usually just enough to get the cones moving.

Narrowed down to those parameters, you can start looking at things like current delivery and such. In a perfect world, and amp just makes a tiny signal louder. What's left is what leads to all the arguments and discussions on forums. We all have to choose our own distortion preference and altered reality.

Having said all that, You can, and many people have filled books with what I don't know or understand about these subjects. 

Among the finest sounding audio systems were those powered by medium powered Class A/B amps such as the classic McIntosh 225 and 240 (for mids alone-McIntosh MC30s).  Generally speaking, low efficiency coupled with low impedance speakers require high powered amps such as most planar speakers to achieve adequate dynamic range.  I had this problem when I owned stat speakers for 20 years.  I have permanently moved to dynamic speakers of medium to high efficiency, despite lower impedance and difficult phase angles because even my medium power amps have great current capabilities and overcome the impedance and phase angle difficulties.  70 Class A tube watts is plenty for my efficient but difficult load (6 12" woofers) speakers in my average size listening room.  35 Class A/B tube watts is plenty for my easier to drive Legacy Signature IIIs in my living room (I auditioned them with a measly 17 watt Sherwood 7100 receiver).  

Funny how whenever I hear Von Schweikert speakers at shows, they have extreme tube power amplification, often with $600K/4 power amps.  Maybe for the huge rooms they play in.  For the typical home listening setting, medium power is required.  As to field coil and other benign speaker power requirements, low power amps will sound best and huge power amps would be energy wasters and possibly blow up the speaker.  

@fleschler

Awesome info above.
I saw your details, incredible wall paneling in your listening room.

Would be cool to see an updated system.

IF you take a lower powered Amp, say 10 watts, running at .5% distortion and run it at 5 watts what is your distortion level compared to a high powered Amp, say 100 Watts and run it at 5 watts output, with .5%. That is not .5% at 5 watts but IS .5% at the capacity of the amp, or at a designated % of output. With a higher wattage capacity you can run the distortion right down to the floor. That is just one of the factors to consider.

This, or one could look at it from a different perspective: say you have an active speaker setup with no passive crossovers and potential steep phase angles - that's one way to effectively make the same amplifier "more powerful"/adding headroom for a given SPL or certainly making more effective use of its capacity with an easier load, all the while making it sound closer to its performing envelope - i.e.: better. Part of that is also dividing the workload between that amp and others to handle their respective and limited frequency spans; in a 3-way setup the amp handling MF/HF is freed of LF which equals lower distortion and better sound. The amp handling upper bass to lower/central mids is freed of everything else = better sound. Sub/central bass amp handles only that = better sound. You could have a blasting crescendo in the lower registers and it wouldn't matter an iota to the amps handling the other registers. With a line level crossover preceding the amps and looking directly into their driver segments with no interfering passive XO's also leaves out any influence of a dividing network seeing the full output power of the amp. All of this effectively makes a given amp more powerful and better sounding for a given context vs. the scenario of it seeing into a passive, not least complex crossover, full-range at that. Active requires more amps (unless running a full-range driver per channel), yes, but this is just to show how the same amp benefits from a given set of circumstances (incl. higher speaker sensitivity and impedance) when it's usually anything but impervious to load. 

One man’s datapoint. Your mileage will vary.

VTL 500 (500 watt monoblock) powering tweeter on a Klipsch Jubilee and VTL 750 (750 watt monoblock) powering the bass on same Klipsch Jubilee. The Jubilee is designed for bi amping and comes with an active crossover. The Jubilee has a sensitivity of 105 db..

https://youtu.be/_7ZGLrOpCQo

https://youtu.be/xUMDlpVu98w

Then the Wotans arrived. Switched the VTL 750 to the tweeter and put the VTL Wotan (1250 watt monoblock) on the bass. It’s not just a bit better, it’s a quantum leap better. Just playing YouTube, man.

Is it headroom or damping factor or whatsoever? Couldn’t begin to tell you. It just sounds fabulous.

Don’t let beliefs stop you. Keep exploring.