I learnt a lot, from just less than half your post!

Did a lot of searching and a bit of reading. Here's a quick summary of what I came up with so far.
Speakers are highly inefficient (roughly 1% efficiency??) when it comes to converting electric energy into sound. To double the loudness or SPL (such that human ear can perceive this as double), one needs about 10 times as much power as before to achieve it. For a 3dB moderate increase in SPL, one requires to double the input power. Hence with higher requirements of SPL, power requirements can tend to drastically shoot up in certain scenarios (as high as 200W per channel). Supplying this high power is not a feasible for most of us. This is where speaker sensitivity kicks in. We can achieve the same 3dB increases using higher speaker sensitivity, 3dB higher sensitivity instead of doubling of power (Since power is a constraint for achieving high SPL).
Also music inherently has high power (higher than average) requirements for short periods, to reproduce certain tones. When power requirements shoot up as high as 200W per channel, if this power is not available at the amp, then the amp output is clamped, distortion can occur! Hence, the amp requires more power for these short bursts.
Also, as impedance varies with frequency, with low impedance again high power is again required.
Supplying high power can he achieved by using a hi quality PSU with high capacitances to store energy. Hence, matching of amp with the speaker becomes crucial and hence a high 'headroom' is desired.
Here are the links, in more detail.
Secrets of Amplifier and Speaker Power Requirements Revealed
The Nature of Power and Dynamic Headroom
The Interrelationship of Speakers and Amplifiers
A nice chart here to visualize better
I have a few questions here about a couple of things.
Max power transferable to speaker is at most half from amplifier. I presume this is why amps tend to heat up. Am I right? So do speakers also tend to heat up somewhere?
What happens when clamping occurs? How does this affect the speaker? I mean since power is clamped, what is the issue except for loss in reproduction of sound?
Also I read somewhere - don't remember where,
'Nowadays matching of impedance to load is not preferred much anymore. Higher efficiency is desired.'
What exactly does speaker efficiency mean?
I might be totally off here, kinda guessing by trying to add one and one.
Does efficiency mean the following..,
With matched impedances, as speakers are not very efficient when it comes to converting electric power into sound, we find a way to convert more of the 'lost power at the speaker' into sound (hence the term higher sensitivity). Achieving higher sensitivity, forces us to compromise on 'not matching impedances', resulting with more loss of power & more heat at the amp??
Feel free to hit me with a hammer if I am totally off
Consider a scenario with amplifiers which are not in the class of hi power amps. For instance I have a sony mini home theater system. It says PMPO 720W

, guess it is about 20W per ch? Of course quality of reproduction of speakers is lower then the kind of models discussed here.
So does all amplifiers in the not so Hi Fi systems range, end up clipping & distorting?
The problem we faced in the high power scenario was in supplying that high power. What about for lower power systems, I presume the capacitance required to store energy is much lower & hence must be pretty cheap. So what is wrong in the ability of these systems to reproduce the sound? For the sake of this argument, am assuming that my lower end amp has multiple drivers in speakers to reproduce more accurately. I have read in many places that the sound cannot be reproduced with the same quality as with higher end systems do. What all am I missing here?