Too Much Power

A problem you can run into is some high powered amps need a bug enough load on the to sound there best. Sometimes easy to drive speakers sound like garbage on a big amplifier as they don't possess enough load on the amplifier. Also generally speaking big amps timing is slower than small amps.

More often than not, not enough power. Got the Parasound Halo A21+, class A/B, 500 watts per channel @4 ohms feeding my PBN Montana XPS speakers and the first 6 watts are pure class A. Not too much heat and packs a wallop.

+1 For Class A or A /AB.. 30 WPC of Class A is plenty for most situations.

Otherwise get A /AB. More user friendly too.

You will never buy a Class D amp after living with either of these.

Aside from greater potential to blow up speakers accidentally, excess power in-and-of-itself is not a problem.  But, in the real world, how one gets there—running many output devices in parallel— could reduce sound quality.  Many years ago, I heard a demonstration of two Rowland amps that were very similar in build, one rated at 50 watts, the other something like 200 watts, running power hungry Magneplanar speakers; I preferred the 50 watt amp, particularly at lower volume levels where the big boys sounded lifeless.  One manufacturer of high end gear touted how his amp used only two output transistors per channel, that is, until market demand compelled him to make an ultra high-powered amp.

I run high efficiency speakers, and with my speakers, the very best sound I’ve heard comes from low-powered tube amps.  One of my amps is an Audio Note Kageki (parallel SET 2a3 rated at 6.5 watts/channel), the other (my favorite) is a custom-built pushpull amp running 349 output tubes (5.5 watts/channel).  I also liked, in my setup, a First Watt J-2 solid state amp that is low powered.  Perhaps I do compromise sound at higher volume levels, but I rarely play my system at high volume levels, and even when I do do, the average output would still be below one watt, and I choose not to compromise that watt with amplifiers that don’t sound as good.

I believe the answer is it all depends. Btw, the answer that a "too powerful amp" endangers the loudspeakers posted above is completely false. I would even go so far as to say that an insufficiently powerful amp is more dangerous to loudspeakers than a "too powerful" amp simply due to distortion being potentially harmful when an amp is overdriven. But why does it all depend? Because different amp topologies behave differently with different speaker loads. In general the answer is "no". While not directly responsive to the question asked, also consider that with most amp designs, more power means more output stages. Some of us believe that less output stages result in purer sound. 

Why is there the oft-dispensed advice to choose speakers first and then the amp? Because if the loudspeaker is easy to drive it may be best to choose an amp that is not overkill in terms of power for that particular loudspeaker. That said, there are other factors that go into choosing an amp for any given loudspeaker. Some of these criteria are just empirical experience as to what mates well in terms of system synergy. That said, when JA of 'Phile measures an amp and concludes that it needs to be mated with loudspeakers of a certain impedance of vice-versa, that advice imho can be relied upon.