My first decent stereo was a Harmon tube integrated, can't remember the model, but this was '71 and it was a few years old. It wasn't very powerful at all, but had blue "on" light (!) and sounded nice with my AR4x speakers and PE (Perpetuum Ebner, or something) turntable and Shure M91ED, I think, cartridge. The PE was a decent table of the Dual type, but a little better.
I also had a Dynaco SCA 35 integrated around the same time.
As with speakers, I think there's no question that amps are getting much better, over the last 15 - 20 years especially.
For me the turning point - the first time I really believed there was any advantage to any one amp over another with similar specs - was the Mission Cyrus I that the salesman almost forced me to take home to compare with the NAD I had which was rated at 3 times the power.
When I first turned it on and put a record on I went to the kitchen to make some coffee and heard the difference even from there. When I came back into the living room I could hardly believe my ears. There was no question within the first 30 seconds that I would be buying it, even though I would be trading down, from a recently bought new amp with, as I say, 3 times the power.
Also, for the previous year I had been wondering what was "wrong" with my system. This amp showed me there was really nothing wrong - now!
From then on I was like an evangelist to all my musician friends, exhorting them to get a decent amp and not waste their time with all the other system details until they had one.
I guess I still follow that general principle, except I believe the speakers are a little more important still.