Nothing to lol about, mains quality effects how well the amplifier works.
If you want an example, play the stereo in your car very loud with the engine off, and you will see the dash lights dipping with the high energy low frequencies, this is presuming it's an older car that's pre-led lights.
It's also the reason why you should ideally plug HiFi components directly to wall sockets, as running lots of components of say a single extension cable creates mains resistance. If not everything to wall, at least use separate extensions for source and amplifier components.
You are conflating so many things here.
You are giving an example of an old car with a poorly spec'd alternator and electrical system that can't supply the load for the car with a high power amp and headlights on.. i.e. the Current the Alternator can produce is far less than the headlights and amplifier require, not to mention the possibility of underspec'd cable that has high losses and hence some voltage droop is expected.
An amplifier in your home is a very different proposition. your house will be fused for 80A or 100A (possibly 60A if looped with your neighbour), your ring main is quite well spec'd (normally 32A), An amplifier, say a Marantz PM6006 draws around 155W @ 240v.. I=P/V = 155/240 = 0.65A.
0.65A is such a tiny load, that even if we assume could well exceed this when it's driving a low frequency note, is still so far under your homes electrical system design it's not remotely in the same league as some old car.. You could plug several extension leads together with most amplifiers and still no where near enough current to even get close to worrying about voltage droop..
Then there is the 'The AC output is a sign wave, but the tops of the sign wave can sometimes be cut off' - Whilst this is possible, the AC-DC conversion and DC rail generation design within any modern and well designed device should easily be able to handle any normal noise/artefacts on the AC, these will be filtered out well before they get anywhere near the rails the audio amplifier circuits will be driven from.
And that's the crux, you are projecting this simple (but not unplausible) effect of voltage droop and noisy mains as if it directly couples right through the device to your speakers.. This should not occur unless you buy some really badly designed bit of guff..
A long time ago you may have had a point, or if we are talking about really cheap and not very hi-fi amplifiers, then sure.. but c'mon, anything moderately well known/decent you don't need to go mad moly coddling.
I've worked with people who design audio amps for Sony as well as some more high end valve amplifiers, this subject has been discussed many times and part of the reason I'm confident in what I say is simply that my day job involves working a talented bunch of engineers that make all manner of medical devices, some having to squeeze every watt out a wall socket anywhere in the world, some measuring signals down to pico-volts.. The biggest design headache is not the AC supply at all, it's just the normal internal DC rail generation, getting that spec'd correctly for the load and noise generated internally is where we spend most of the design effort, the actual AC-DC conversion with modern power supplies gets rid of anything you are ever likely to see within your home.
I am a bit of a basshead so a sub is more of a priority, but interestingly, songs like 'Hey Now' do have this amazingly layered/detailed bass, it's such a brilliantly engineered song and whilst the desktop speakers give a good sense of the bass, it's on a whole new level with the sub. Mind you, since I am 'near field' this is a different proposition to a larger room in a normal listening position, a sub will still add a bit of a new dimension but you need something much larger/more capable IMO.
