Yes, the majority of the time I suppose, but not always. Sometimes I just like to move mouse around timeline and zoom in to check various areas in the timeline, ie just looking around at the various timeline clips, not looking at the player.
I’m not sure which zoom center is best actually. I would need to spend a little time with the way you suggest, to get a feel for it. I’m sure the playhead as zoom center would be fine.
I used to use Kdenlive a bit, so I got used to the feel of zoom center being under mouse cursor.
And yes, a nice coincidence about something like View> Fit to width, or Zoom> Show All,
(I think preferably with a hotkey combination), to see the whole project instantly.