Exactly. Where I live in Oakland police lapel cameras have been required for a while, but there's never footage when cops are accused of abuse.
Part of the problem is technical, lapel cameras don't have infinite battery and they don't have a wireless connection. That means that the cop has to remember to turn it on and off and he has to upload the video. Both provide the street cops with opportunities to not make video available.
Your public streaming idea isn't really that easy technically. Each cop would have to carry a smartphone with a large battery pack to pull it off.
Then there's the endless footdragging when you try to request the video which provide police management and district attorneys with ways to not make the the video available unless you're really persistent and have a lot of time.