Why do speakers improve with more powerful amps?

It’s about the ability of the amplifier to deliver transient response to whatever speaker they’re driving. Transient response can take loads of power momentarily. If your speakers are efficient enough to handle that from a low watt tube amp then great. I have found that most speakers require a lot of power to reproduce transients properly. Play London Grammar, “Hey Now” and tell me if your amp has enough power to handle it.

Try driving a set of Maggies with a 2W Decware Zen Triode. Not going to work. 

Not having to deal with the interaction between driver impedance and passive filter network gives the designer of an active crossover/equalizer much greater freedom and control to develop a superior product.

As some one who can do both, this statement is not always true. Depends. For certain, the digital/active domain makes time delay easy, which therefore makes high order, symmetric crossovers a lot easier to accomplish on a flat baffle speaker.

@Phusis

This shows how easily it is to ignore the Facts of the subject and keep on trying to reinforce the idea that clipping is the ONLY place that headroom affects. Clipping is only a minor concern is is the LEAST of the actual AUDIPOPHILE reasons for having overhead.
Yes you can power a pair of headphones with a couple of well designed watts of power but you won’t be powering a set of Maggie’s with only that. You are mixing apples with oranges IF you think there is not a high level of sound quality in reference here. Or as I said before would you expect audiophiles totally ignore ALL of the statistics published about the Amps they are discussing or buying.
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.

Possibly if I make a comparison to mechanical engineering. A simple street car capable of 150 HP putting out 100 HP is going to be under far more stress and pushing harder on every last component in it than a muscle car capable of 500HP putting our 100HP. The muscle cars is barely idling and not under ANY stress.