I wouldn't think that there'd be anything to gain, with lots of things to lose. It wouldn't make any sense in my opinion.
Some of the concerns would be (most of these aspects mesh together):
--players distracted
--cameras everywhere, which could show something that they don't wish to share, along with it being a pain in the butt for everyone involved
--added drama for bubble players who are competing w/ each other
--disclosed injury statuses for glimpses of guys in the training room
--a bigger learning curve/development time for rookies who aren't fully getting the message and a real look at what the first NFL TC is really like
--a bigger target and more unnecessary news coverage for a team trying to stay low key