RV, I have repeated your experiment a number of times with the same results. On longer always sounds better, but with diminishing returns, for about a week.
Its’s true of my DIY phono/pre - it’s on all the time. It’s true of my DIY Class A amps (they idle continuously at half power). It’s true of my Bryston SST in the HT (although B recommends turning it off). But since HT doesn’t matter nearly so much, I do turn the B off, and then back on an hour before - but an hour isn’t really enough.
My cartridges take 10-40 minutes too.
As for the car analogy, I ALWAYS used to warm up my engine carefully, and my tires too, before taking a fast lap.
YMMV