Allowing rebinding of keys, requires that the key bindings be stored somewhere for permanence, and requires that they be loaded before play starts.
Think about this a moment on a console. You have a system that has storage, yes-- but that storage is intended for saved game data. There is no system-wide storage medium, like say, the system registry. As such, when the game first launches, the only media it has is the game disc, which is read only. EG, when it first powers on, it needs defaults on buttons, so that you can navigate menus, etc.
Before you get cocky with me on this-- XBOX and pals are designed to be multi-user. saved games are already separated by which user is logged in. The system does not allow general read/write to the hard disk. (GoD containers on the XBOX are read-only as well, so dont get ideas. This is a security measure to prevent hackers from exploiting the container, and simplifies the digital signature system used to verify that a GoD container is legitimate/not pirated.) SO-- to have custom key bindings, the ONLY place you can store that is *gasp* INSIDE A SAVE FILE.
You could go about this the Capcom way-- have an annoying "system" save that on first boot, gets created, and loaded with default keybindings that the player can set later-- and on subsequent startups gets loaded immediately. (this is how Monster Hunter Tri does its thing on Wii, for instance.) but most XBOX games do not do this. Presumably this is because of the filthy casuals who just want to play immediately, and dont want to bother with remapping the gamepad, who apparently are a pretty large portion of the gaming demographic.
Just saying it is not as straightforward or simple as doing it on the PC is, where you can just write an XML file somewhere with the binding schema, and have a nearly inexhaustible supply of potential binding layouts ready to roll. (because HDD access is cheap and effective.)
When you couple that access problem, with the problem with casuals and load times, with time constraints and budget limits in game development, the use of a bog-standard set of loadouts becomes the lowest common denominator that gets used.