Shouldn't this be basic procedure for any object in containment?
I like to imagine that some safe or trivial items are just kept in lockers in the same room, or piled up in a warehouse situation. If we classify it as safe and it doesn't need special attention why waste the space and resources?
Are these little things really so loud that we can hear them breathing?
If they are loud and talented enough to mimic a TV they are loud enough to hear when they're idle too.
Why not? Why couldn't he just show them?
This is about the paranoia of a guy no one would believe. He WAS crazy, but there WERE little men in his TV. And no one believed him because his condition was bad enough to keep people from hanging out or paying a lot of attention to his TV set. That's the hidden back story; a lonely, tragically disturbed man. Someone could have noticed and the Foundation could have swooped in right away to contain the set but that wouldn't have the same implications.