Out of my collection, I own 11 Les Pauls. I gig regularly and I usually play a different guitar each show.
I’ve only had one guitar fall over.
A few weeks ago I accidentally pulled on the cable while the guitar was on the stand and it fell. It actually rotated on its Y axis with its back facing the fall and the headstock hitting the ground. There was no break or any major damage.
I was lucky.
It’s popular belief (and knowledge) that broken Gibson headstocks are the majority of guitar repairs. Since the neck is all one piece, the angle produces a fault line regardless of how strong the wood is. Not to mention the truss rod hole creates even more of a weak spot for the neck to break.
This does not deter me from being a Gibson fan or suggesting someone buy a nice Les Paul, ES-335, or SG because they all essentially have the same neck and headstock.
But Gibson guitars aren’t the only one with necks that break. For example, there are plenty of Strats out there that have been accidentally dropped or fallen and the headstock snapped completely off.
Obviously, being very careful not to drop any guitar is your best bet.
I’ve added photos of the guitar I dropped. It’s my Alpine White Les Paul Studio. It escaped with only minor scratches.