It had darn well better have some relevance to feet. Because you can bet that no DM is going to answer the question, "how deep is this pit?" by saying "12 squares." Nor is he going to answer the question, "how tall is the wall?" by saying "three squares." Without a three dimensional representation of squares those answers are not helpful in letting the players imagine the scene. (Is a three square tall wall tall, short, or what?; If I say the PCs are trying to fight their way up the Tower of London, how many squares tall should the walls be?)
And when a PC falls down that sixty foot pit he is certainly going to want to know how much movement it's going to take to get out (flying, climbing, or whatever). So we'll need some kind of feet to squares conversion. For that matter, the PCs who didn't fall down that 12-square deep pit (assuming for the moment that pits do get depth measured in squares) will want to know whether the 50 feet of knotted silk rope they have with them will reach to the bottom and let their friend climb out or if they will need to tie another length of rope onto the end of their fifty feet of rope so that it reaches to the bottom.
For that matter, PCs will also want to be able to estimate how things will look on the grid even when they don't have a grid. Let's say that the PCs are receiving a report from a scout (perhaps a familiar). The scout is describing the ruined fortress that the hobgoblin horde has inhabited. He says that the hobgoblins have cleared a glacis around the walls so that there is no cover other than short grass and one dilapidated shack between the forest and the walls. "So, how wide is that glacis?" the PCs ask. You can be darn sure that the scout isn't going to answer "thirty squares." But when the DM answers "about 150 feet" the PCs are definitely going to want to be able to estimate how long it will take them to cross it and whether or not the ranger is likely to be able to pick off the sentry on the wall with a bowshot or if he'll be out of range.
The rulebook may or may not express all horizontal distances relating to combat abilities in squares. But even if it does, odds are very good that vertical distances (which are generally not represented on a battlemap) will be expressed in feet (as the pit examples from the design and development articles indicate). And even if they weren't the fact that our imagination and narration works best in real-world distances means that we will need a reliable conversion mechanism in order for it to work.