Yet my impression is that the rapid list is volatile and often not reflecting the reality, the classical rating is better in tune with actual strength

It's the opposite - classical ratings is more reliable because there are regular organised events while there are very few serious blitz and rapid events. Most top players only play the rapid and blitz World Championship, no other events in these time controls.

You're right about the number of games influencing the rating volatility but the length of an individual game has nothing to do with it, it's about how many events are played how often.