Let's see, what's the difference between having more corridors, and more staircases instead of a turbolift shaft?
Wouldn't a corridor and more corridors and staircase(s) take up space as well?
Your reasoning is non sequitor. You are saying that turbolift shafts take up space, but to replace them by corridors which also take up space.
an imagine is better rhan 1000 words:
You may have misunderstood that drawing... Here's the same trip you tried to plot, using brown for the corridors and blue for the turbolifts. You can see the turbolift is a way more direct route. To go on foot, you have to cut through the Rec Deck! It seems like, at least on this version, the designers are assuming that turbolifts are the primary means of moving around on the ship.