There are many and varied reasons why valve amplifiers sound so good, some of which are not fully understood even today. In the same way that many expensive solid state designs don’t sound as good as expected.
Valve amplifiers are comparatively simple. With a shorter signal path and fewer components to preserve that delicate audio signal intact.
This gives the opportunity to use much higher quality full sized components (not tiny surface mount), e.g. resistors, capacitors etc.
Valve amps sound better if constructed without using printed circuit boards which often add noise, distortion and can degrade sound quality.
Valve distortion is very benign and less noticeable compared to solid state which even at very low levels can be noticeable.
Valves have a much greater overload capacity than transistors, essential as music is so transient.
This gives massive ‘headroom’ so the loud passages can be reproduced with distortion.
Valves are more musical than transistors giving more ‘colour’ and emotion to the recording.
Valve amplifiers ‘warm up’ much quicker therefore sound better without a long wait.
Valve amplifiers generally use little feedback unlike solid state which is often much higher.
Valve amplifiers have a much smoother sound than solid state without losing the detail.