My personal take on this is that the bridge is made up of a series of consoles which can be arranged in whatever configuration you like. You could, in theory, put the main viewscreen complex (including the two status-monitor panels flanking it) immediately next to the lift entrance... and I suspect that a few captains might prefer things like that!
I'd guess that under April, the Enterprise had the "original intent" arrangement, but that at some point, one of the commanding officers got sick of having people walk into his bridge DIRECTLY BEHIND HIM... giving him that creepy "someone sneaking up on me" feeling. So, they unbolted the consoles in a dockyard at some point and shuffled them around to let the captain look over his shoulder at the entrance.
Not a TRIVIAL change... you'd have to shut down operations on the bridge for a day or two, minimum, in order to do it... but not all that complicated, is it? Especially if you think of each station as simply a computer terminal which is tied into the main computer (which I treat as starting directly below the bridge on deck 2).
Again... the main viewscreen isn't a window, it's a computer monitor. It can sit wherever it's most convenient, and there is zero logical justification for saying "that has to be on the centerline of the ship."
I like this take. I myself wouldn't want people walking in behind me, either.

And for a real world example of something similar, most submarine drivers face to the side.