Bunny Safety Issues - advice please!!!

I was just wondering, is there much chance that my rabbit could hurt itself??? Basically, I put him into his cage whenever no ones at my house and at night. However, I would like him to have more time outside. The area where he is allowed out is quite large and has a sofa against a wall, a table, chairs and a beanbag. I have rabbit proofed all thats possible but is there still a risk of him falling of the sofa or table??? What if he does at night or when no ones there? Also, he goes crazy when he's on my bed in my room - once he fell off and was a bit dizzy afterwards. He binkies and whizzes across my bed. How likely is it that a rabbit will hurt itself or how likely is it to be life-threatening if they fall off something??? I am just worried that my rabbit is not getting enough time outside but I am also worried about the risks.

Please just give your opinion: Should I let him have free run of the house when I am gone and at night?

Extra info: Mozart is a very, very active bunny, he binkies and races across and over all obstacles. He is very shy and does not live with another bunny (he has not had good experiences with bonding). Also, he is a very cheeky and sometimes naughty rabbit - always taking risks and sometimes aggressive/angry when he doesn't get what he wants. But overall, he is very sweet and loyal to people he knows.

get some puppy pens and make him a compound. i do that for mine. they can run about without coming to harm or destroying anything.

A play pen sounds like a good idea to me too, they might be naughty if un supervised for long periods especially in a larger area which might not be bunny safe