I see this explanation often when it comes to amplifier power, and you explained it very nicely, but there is something about these calls for power that doesn't fit with the real world experience of many of us. Many have used relatively low powered amplifiers for decades, including tube designs, that would be clipping constantly in the commonly described scenario, but it's not a frequent complaint from users of low power equipment. There are plenty of listeners out there happily working with 20-60wpc without problem. If my use case only calls for 40 watts why do I want to pay for double the power?
Also, using the peak SPL calculators, the OP can achieve peaks at 101.9db from 45wpc when seated 10 feet from his speakers, which are quite insensitive. That's more than enough to wreck one's hearing in short order. The 'more power' discussions never get me past the question why I would ever want to make more peak SPL than that, nor why I would want to pay for more power than I need in my situation.
My own experience is that I listen at low levels, rarely above 60db, with 70-ish db being damned loud (to me) in my room. I'm using less than a watt most of the time and accounting for peaks probably never using more than 20-30wpc. I've had 'big iron' 200wpc amps in my main system and it became clear that, beyond weighing a ton and taking up lots of space, they were largely wasted on my system.
My current main amp is a Dared VP-20, an 18wpc 6L6 push-pull design that drives 92db sensitive JBLs, and my listening never even pushes the Dared. I understand there may be momentary instances during which the amp is 'soft clipping' but I never hear obvious distortion and there is plenty of volume/power left during normal listening. Not long ago I was using 90wpc and 100wpc before that, in the same system. The bigger amps neither provided enhanced 'grip', tighter bass, nor ease of delivery, things advocates of big power often describe. I think for the listener not rocking out (and wrecking their ears and making their neighbors hate them BTW) there just isn't the need for power so often pressed.
Unless driving extremely insensitive speaker loads, I suspect that most of us are likely to be using one watt or less most of the time.
Not a call for "more" power. Rather, it is an endorsement for enough power...enough to achieve desired loudness with the speakers being used, without clipping distortion, at desired listening distance.
Might be 5 watts, might be 50, might be 500.
The OP mentioned wanting to explore the idea of using a higher-powered amp. I was not advocating for or against. Just explaining one of the key relationships between power and sound quality.
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