From a purely practical standpoint, codebases like this (I have 20+ years in the console games industry as a programmer) contain source code, headers, and other proprietary stuff from other vendors (to say nothing about the console SDKs) we're not allowed to just release. Finding it all, ripping it out, and being confident it's been done properly from a legal perspective is expensive, cumbersome, and risky.
Watch the opening screen of a modern AA to AAAA videogame these days. It's littered with 3rd party software. A multiplatform console game that was never intended to be open sourced is not trivially open source-able.
Also, EA gets to keep it, because it may be of value to them down the road. (I mean, probably not, but that's what they'd say. They own the work.)