1) I don't think I can recall hearing flutter on any of my turntables, going back to my early synchronous Garrard decks. Or belt drive machines (AR and Thorens). Certainly not with servo direct drive, and definitely not with quartz PLL DD.
Interestingly, I notice speed drift (but not wow or flutter) on my mechanical idler-driven record player from 1970, but I am only aware of it because in single play mode the strobe drifts a bit over the course of the record. In changer mode, with two discs on the platter, drift is more noticeable. I presume this is due to the way the idler 'slips' or moves up or down on the tapered brass motor spindle (that is how the deck offers speed variation). However, the drift is slow, and I do not perceive it as a pitch change over the course of the record. Possibly someone with perfect pitch would notice. On a servo or quartz DD turntable this sort of drift would not likely ever be an issue.
2) Your point about digital is well taken, but perhaps different for the recording engineer, as opposed to the home record player listener. For analog production, high speed open reel tape was used (discounting the not often seen direct to disc recordings). Perhaps flutter was/is an issue for them, with certain tape machines. Obviously this is cured by digits. However, my records cut from analog tapes don't show audible wow/flutter, so whatever the engineers were doing to attack this problem (if it was a problem) worked.
That said, I have heard speed variations on many consumer grade open reel tape decks, especially at low speed (3 ips), and especially if the tape is old, prone to sticking. This would not be an issue in the studio. Generally, with consumer open reel, at 7 ips I never heard any speed problems, unless the deck started to malfunction, which happened more than I'd like to have ever experienced. All my decks eventually needed some kind of service, whether they were from Teac, Akai, Pioneer, or even the more expensive ReVox (A and B77).
Toward the end of the consumer open reel scene, the higher-end Technics decks featured quartz PLL direct drive motors, with closed loop dual capstan tape path. My guess is they were likely the best of the bunch, as far as speed stability went, but I never owned anything like that.