The BBC should open source most (if not all) of its developed technology

Following on the Recipe for disaster post on the topic of BBC to close recipes website as part of £15m savings, I wanted to put down this idea, which in my view, goes to the heart of the value that public entities (like the BBC, but also the NHS, public services, Non-profit orgs, charities, etc... ) should provide to society:

The BBC should open source most (if not all) of its developed technology 

The BBC hires a large number of software/application teams (from Devs, to QA, to Designers, to Architects), which create a large body of code, that is in most cases behind closed doors and not available to the general public (namely other public or private organisations that would benefit from that code)