Here's my personal "in my mind" explanation for the offset lift door in TOS....
The actual turbolift
shaft is in fact directly behind the bridge, in line from the center of the viewscreen through the centor of the bridge, through the captain's chair, etc. (and the captain chair and viewscreen are in the center along the long access of the ship).
However, the door leading to the lift car is not along that centerline, and that's because the lift doors we see
do not lead to the shaft itself. Rather, each lift has multiple cars, and each lift stop has a little alcove in the shaft in which the cars -- upon reaching their destination -- slide "sideways" into before opening. This allows the shaft to stay clear so other cars could use it.
So the doors we see outside the lift are the doors that lead to the little alcove in which the lift cars slide into after arriving.
This also allows multiple cars to be waiting at the bridge so if one person got in the turbolift at left the bridge, another car would immediately slide into place, allowing someone to use the lift right away without waiting for the car to return.
Again, this isn't necessarily true in-universe, and maybe only true in my head.