Yes, every track has a different matching point, you're quite right and that's the attribute of bpm most difficult for computers: which peaks to count? Manuall

Yes, every track has a different matching point, you're quite right and that's the attribute of bpm most difficult for computers: which peaks to count? Manually pre-setting tracks has to be very consistent too -- if you pick claps on one track and go for snare on another, claps might bias the upbeat and snare the downbeat and when Ableton matches the tracks the kick will sound off. That's the problem as you identify: any two tracks may have a sound that matches best for that particular mix point, so it might need to be adjusted live. But if you are adjusting tracks live by a few ms... It sounds like you have learned beatmatching and are using it! To your other point: analog turntables, especially 1200s in good shape, do not drift. A proper beatmatch can and should ride the whole track. Multiple manufacturers make turntables of this quality. The error you saw was either poorly maintained equipment or an inexperienced DJ.