A vintage type amp still works fine at full load though, can put out continuous max power until they run out of notes or whatever.
The HT supply doesn’t differentiate between a continuous single note and an continuous stream consisting of different notes; full load is still full load, I don’t see how the HT cap type would make a difference?
That's not what I said, it's not about full power. It's about sag, compression and not rounding off the very front end, the initial attack, of the notes envelope. I also said SS rectifier. You can still have full power and be well into the amps PSU sagging, the OT compressing the far ends of the frequency spectrum more and more and the speaker into compression too. In fact you get more power as the sine wave squares off. As this happens the very 1st pick attack gets more and more lost, diminished, yet you can still have full power output.
It's a matter of feel. You have to get behind the wheel and play through the amp. Some love 'grezzy' amps, weak PSU, squishy/saggy amp. If you can have that end of the spectrum of an amps feel, you can have the other end too. Amps are tools, and as such can be under-powered or over-powered for the job.
A friend of mine and I were A/Bing speakers 1 time. When he was playing I could hear some difference in sound/tone, but nothing drastic. But when I got behind the wheel, there was a huge difference in how the speakers responded to pick attack.
Another time, had a BF Dual Showman, had a gig, set up, turned on the amp, something was wrong. Sounded odd. There was a guy who came to see us and sit in. He was playing 2nd guitar for Buddy Guy and Jr. Wells, had played for them for several years at that point. He got up and played through my Showman, after I asked him if he thought the amp sounded odd, he thought it was fine.

And he was a Fender BF guy.

I took the amp into the shop, before I worked on amps. One of the 6L6GC's died. I heard it, he didn't, my bass player didn't. The bass player played with me for several years, so he knew that amps sound.
Depends on how you play, what style you play and how developed your style and ears are.
I had a Mesa MkII C, never liked it, way too stiff for me, too articulate, I could hear the smallest little pick attack thing, extremely unforgiving. The least little subtle pick mistake, you could hear it. Now some guys would love that. And I played a BF SR for years, main amp, not exactly a weak PSU in those those amps. But certainly more grace than that Mesa.
How do you explain this? This was way before I had read anything about PSU's, sag, etc.
Do you play? It's in the hands, ear, not paper that you get to know these things.