I will never understand why they don't put live feed online. They could intercept it with adverts and possibly even take a little more from the sponsor for having their branding plastered all over it. Moreover, if they're not willing to do it for free then make it a subscription service akin to BB11.
The real reason we don't have live feed has nothing to do with cost. The real reason we don't have live feed is because the producers want to ensure they can manipulate everything and have an environment which is artificially managed with as little in common with the original concept of the show as possible. Without live feed they have been able to send housemates out for magazine interviews, send producers into the house to manage tasks, and even let people s**t in the kitchen appliances with no repercussions. THIS IS WHY THERE IS NO LIVE FEED.
EDIT: After posting this I realised that the first sentence I wrote was incorrect; it is infact quite clear why there is no live feed.