Leashes among surf paddlers are more controversial than rudders verses skegs among other paddlers. I have often used leashes in the surf with my sit on top to maintain contact with my boat. I've been over the falls many times and yet to have become tangled. Of course my experience is different from many; I grew up sailing Hobies through the surf where being tangled during capsize was a much greater risk and more common occurrence.
I understand the the ACA recommends that you never use a paddle leash in moving water. This would include rivers, surf, and anywhere big waves happen. I do not know the BCU position on this, but I'd expect they be against it as well. On the other side of the argument I see that many surf ski paddlers and sit on top paddlers use them.
Personally I'd like to have the choice of maintaining contact with the boat and without the leash I rarely have that choice. I miss my brace on a wave or get tumbled over the falls and the next thing I know my boat has washed away and I'm swimming with the paddle as fast as I can to catch it. If the waves are breaking there is no chance of me swimming fast enough to catch an empty boat. Of course I do notice that in a sit inside this never hap[pens because I must make a conscious decision to leave the boat and I have always been able to have one hand on the cockpit and one hand on the boat. Apparently waves have to be much bigger to strip one out of a sit inside cockpit than from the thigh straps of a sit on top.
One article I like is here at my favorite online shop: http://www.topkayaker.net/Articles/SurfSail/SurfLeash.html
I'll find other articles and add them later.
I'd be happy to hear your views or read any links you can share on the topic.