250 watts: why so much power?

More important than playing "extra loud" is the ability to play music at a moderately loud level without the clipping distortion and compression you would hear when using an amp that is not quite up to driving the speaker load. Its not all about your amp playing louder, just being able to handle the demanding peaks and keep control during complex passages.
Another dividend can be improved bass control and quality. Some speakers dont need much power but still respond in the bass region. Matching the speaker to the amp is the most important aspect.

I leave my amp on all the time. Will a 300 wpc amp consume about 3 times more electricity than a 100 wpc amp when idle?

Also, a speaker with 8 ohms impedance harder or easier for an amp to drive than a 4 ohms speaker?

More power hopefully mean a more authoritative and controlled sound with more of a relaxed ease in the musical presentation with greater and more life-like dynamic swings. By relaxed ease, you do not feel that the amplifier is pushing it's limits as it's just humming along beautifully.

But all the above can certainly be accomplished in a lesser powered amp to a certain degree. Generally, it's just cheaper and more conventional to add more wpc.

Ulimately, the wpc is only one of many factors that determine whether an amp is worth living with.

But still wouldn't want to be without those wpc's. At least not with my current speakers.

-IMO

Matchstikman--to answer your questions to me: (1) there are simple formulations as to efficiency. If I remember correctly, and I'm a listener, not an engineer, speaker efficiency is measured in decibels of output per watt of power input. Speakers rated under 90 db. are considered more or less inefficient, over 90 more or less efficient. But it's more complex than that: my speakers were just upgraded, and while their output rating only increased by 2 db., the manufacturer's power recommendation went from 200 watts per channel minimum to no upper limit to 30 watts minimum, 300 maximum. Inefficient speakers driven with inadequate amps tend to sound opaque and closed in. The inevitable tendency is to turn up the volume at the preamp, which only makes the problem worse, because the power amp is now working even further outside its comfort zone. My own experience is when I have added a more powerful amp or switched to more efficient speakers, I wind up listening at a lower volume because more detail reaches me, both on quiet passages and loud ones. (2) I listen at a volume I can get away with in a New York apartment, which isn't all that loud. (In fact, I use a 4-channel system, because the rear speakers increase the sense that the sound is filling the room without my having to blast the overall level.) (3) 22 X 13.5 X 9.

Paraphasing the better explanation:

the ability to play music at a moderately loud level without the distortion and compression you would hear when using a lower powered amp that is "clipping". Its about your amp being able to handle the demanding peaks and keep control during complex passages

Ideally the available dynamic headroom should be in the neighborhood of 20dB, a power multiplication factor of 100 times. So if you're running at only 2 watts per ch. average power, then you need a 200 w/ch amp to have 20dB of headroom & stay out of clipping. You don't use all of that amplifier power continuously, but you do need the large power reserves.