The more “high end” you go in amps, the more “difference” there can be. But these differences are intentional by design (sometimes also buy pure incompetence), because they want to sound different from the competition (and hopefully be perceived as “better”).
I have come across/read about amps with intentional high second harmonic distortion (tube like sound), solid state amps with very high output impedance (low damping factor),amps with a rising response towards high frequencies, rising low frequencies, amps with a pronounced mid range, etc…
Sometimes you also see very high power amps with very low THD specs, but they only quote THD at nearly max power. During normal listening barely 1 watt is used, and sometimes such amps still suffer from quite a bit of cross-over distortion making THD specs at 100mW a lot worse and potentially hearable! So watch out for those also.
So I must say I agree a bit with both parties here. The well-designed amp problem was indeed solved quite long ago, but finding one is not always as straight forward if you are in the ” audiophile world”. Typically low end mass produced gear is much better is this, because they just use design from the application note and that is it. But sometimes they do indeed suffer from too much price cuts, so they also are not good.
So, in my opinion, buying the more expensive (250€) mass produced low end amp from the typical companies like Marantz, Denon, Sansui, Yamaha, etc should get you an excellent amp. Another approach is to carefully look for detailed published specs. I like to see THD vs power, THD vs freq, output impedance vs frequency and IMD spectrum. Typically when this data is available the designer want to show they have a well-designed product. Unfortunately pushing detailed specs is something that is not common, and the typical argument is that they “do not mean anything”, while the contrary is true off course… DIY is for sure also possible, but unless you can use salvaged parts, is a lot more expensive that a mass produced amp (but also lots more fun!)
As to speakers and acoustics, this problem is not solved at all for the moment, mainly because to the major impact of the directional behavior of the speaker, and its corresponding interaction with the room.
Maybe with active speakers and lots of DSP power, we will be able to steer directivity of the sound better (with still a reasonable sized speaker), allowing to have a more predictable sound quality in the future.
So, if looking for a technical challenge, this would be were a invest my time in. I have built an automated rotary table to measure the directional behavior of my loudspeakers, and the more you measure this, the more you appreciate the shear complexity and trade-offs in trying to get “good” directional behavior. “Good” means a good match with the room they will be used in, so this makes the challenge even more difficult.