This is the beauty of audio
Ultimately it can not be measured. this is an art
This is interesting. PSU is very important, even I can tell because I rolled some rectifiers tubes an amps I had and results were astonishing. However, some of the widely recognised amps do not have tube PSU: Euforia or La Figaro 339 to name a few. The amp I am using currently Ayon Ha 3 is also solid state recifier. I was told solid state rectifier gives well define bass, which is good for Meze Empyrean. What is real difference between solid state/tube rectification with respect to sound?
Some more comments as you asked. Firstly, even though I may write as if black and white, in fact I'd say it's more like shades of grey.
The ideal rectifier does not exist.
Ideally it would start to conduct with the slightest forward voltage; it would have zero effective resistance; and it would turn on and off completely cleanly.
The amp designer has to accept the shortcomings and take steps to minimise the problems, and develop his item to get good sound. There is a name for this process; engineering!
The amps quoted above, and many others besides, have been very well engineered and I have complete respect for their designers.
I'm not an expert in the subject but here goes about the differences.
Solid state rectifiers have the problem that they do not start to conduct until the voltage across them reaches a threshold (about 0.6V); then they turn fully on rapidly. This gives a sharp transient; the current flow will be jerky as a rough term. This has quite a lot of rather nasty high frequency content (hence the term 'dirt'). A good power supply will suppress most of this, and results can be very good. But perhaps not the ultimate in terms of lowest possible noise floor.
Also, when a SS rectifier turns off, it can generate a reverse spike, again with nasty high frequency content. Schottky diodes minimise this, and sometimes small capacitors across the diodes are used to kill it. Again, results can be good; but perhaps not the ultimate.
Valve rectifiers start to turn on gently as soon as there is a forward voltage; and also they turn off cleanly. This means they are clean (no HF spikes, no dirt). Hence the generally good tonality and sound quality. But they have a drawback; unlike the SS diodes, the voltage drop is not constant but increases with the current. In effect they have an internal resistance. This can result in compression of the sound. This may also affect the bass, as users mention some loss of bass quality.
A good designer will work round these problems to minimise them - I won't claim to be more than half good
but I do OK. From advice of Tube DIY Asylum I have found damper diode valves with low voltage drop; and sometimes I use them in parallel to reduce the equivalent resistance.
Valve rectification costs quite a lot as usually a larger mains transformer is needed, as well as the other extras.
Remember that every £1 on components has to add £10 to the selling price and now you can perhaps understand the designers' problems and choices. Given these constraints, I'd say they do very well to achieve a good compromise giving the fine quality they do at affordable prices.
Tastes and preferences also come into it. Myself, as you probably know, with my liking for gentle jazz and female vocals, I want to hear Halie Loren and Laurie Allyn etc in my room; hence my love of valves. Others may validly prefer a good valve amp with SS rectification.
My kind of virtually no compromise PSU means say another £50 on the mains transformer, say £150 on chokes, perhaps £100 on caps and other bits. This would add perhaps £3000 to the cost of your amp .... no wonder it is rare. But very, very nice sounding, I assure you.