The problem is that the track browser acts like a filter, whilst the a-z bar doesn't. Eg.
Clicking 'J' on the a-z bar takes me down to 'jimi hendrix' in the main pane, but the library is not filtered; I can still scroll from 'J' through my entire library. If, as you suggest, the track browser was synchronised and therefore highlighted 'jimi hendrix' in the album artist column, then because it is a filter, only the hendrix albums would/should be shown in the main panel.
Using the track browser filter, you're supposed to start off with a general filter on the left hand side, and get progressively more detailed moving toward the right.
The library explorer is also a filter, so again syncing the a-z bar with it would not work either.
Note that the track browser and library explorer *are* synchronised with each other.