Very nice theory, wouldn't have thought of that myself.
The only other thing I think of at the moment is this -
It symbolizes Frank's restraint to his wheelchair after Sewell injured him beyond repair. Forever rocking back and forth, doomed to be a vegetable for the rest of his life. If you think about it, there's a lot of bloody chairs in that game! The wheelchair on top of the roof, the two "skid marks" of the wheelchair that you follow, the one stuck in the lift, and even using chairs as a weapon!
Of course, as you know, I'm sure... the Born Free song comes from the scene where Sewell walks off in a flashback away from Murphy's cell and starts singing it to himself.
"Born Free" could also be a taunt against Murphy - since he isn't really free from his cell throughout the game (he's still a prisoner) and he isn't free of his guilt.
Very interesting view on symbolism, though

Nice one! Then, of course, there's the toilet flushing, which I always saw as -
Murphy flushing away his past/guilt/the shit that wont free his mind.
TTWD