The safety reasons don't hold, you can easily shoot from several kms away (there are people on land several kms away from the launch pad). In the worst case, you can pilot a drone from several kms away, close enough to the barge.
> any ship that far out is going to be using a commercial satellite data feed
The footage from the droneship always appears perfect seconds before the landings. So it's not simply the fact of being at sea.
To your second question, how about a camera on a boat closer in with a hard line to a boat farther out with the satellite connection? You act as if sending a video feed is an unsolvable problem despite them beaming living video through the rest of the mission when they are in space.