Nor indeed does each platter even have the same number of tracks at the same spacing in modern drives. Ever since embedded servo became the norm for hard drives (late 80s), there hasn't been a need to align each platter with the others.
Incidentally this is why a HDD with a bad head or media area will make clicking sounds, sometimes very loudly, as the head actuator slams against the stops since the controller can't see the signals it's looking for and can only sweep the surface in search of them.
Have there been attempts to use active cooling/heating (i.e. thermal sensors combined with piezoelectric effect elements embedded in the housing) to maintain a precise, consistent reference internal operating temperature, as a means of eliminating the need to accomodate thermal-induced drift in tolerances?
What you and others are describing is strikes me the way that opening up the package of a modern memory chip and finding a fabric of millions of tiny magnetic cores would, rather than a silicon array of capacitor/transistor cells - that for some reason no fundamental rethinking of the problem has prevailed and thus the only developments in RAM for almost half a century is miniaturization of what was being done in the 1960's.
I wouldn't call that "the same basic mechanism" as there have been lots of refinement over the years, but it turns out that having the heads themselves find what they need to read was the best solution.