Now regarding the function of these knots. It seems to me that multiple nip turns are more "useful" than multiple collars.
To me, there is a ratio of collar tension to nipping power, and that translates to a ratio of collar tension to load. As the load gets stronger the nips nip tighter but the collar requires more tension to hold the nip straight and closed. I guess if there is any (non security related) improvement needed over a standard bowline it would be to increase the ratio of nipping force to collar tension, thus reducing strain at the collar. It's not clear to me that a standard bowline really needs any improvement in that sense, but ok.
True full multiple collars as in a True Double Bowline [1] or similar[2], reduce the tension per collar, but not directly the total collar tension. They should also increase the nipping force by way of having more load carrying lines actually nipped, and so this, in the ratio, reduces collar tension. They do soften the bend of the standing end around the collar for what it's worth.
Fake double collars[3] also have the softening effect, and they create
a little of their own extra nipping force, friction preventing slippage around the collar and thus adding to the force of the nip to prevent slippage of the tail (or slippage between multiple loops) but I guess this is much smaller than the added nipping force of the nip for true double collars.
However, more nip turns should directly multiply nipping force too (since collars should be relatively less tense anyway) AND they provide more torque on the nip (because the nip is longer) to keep it straight and closed, thus reducing (I guess significantly) needed collar tension.
So, I'm not at all sure that I agree that improving collars is better than improving nips. I would think we should aim to minimize the importance of collars by decrease the tension required of them and by nipping better to prevent slippage.
On the other hand, I'm not moved by any of it if it doesn't provide more slack security. The bowline is already good enough under load isn't it? Why complicate it?
1.
http://igkt.net/sm/index.php?topic=5385.msg36532#msg365322.
http://igkt.net/sm/index.php?topic=5385.msg36534#msg365343.
http://igkt.net/sm/index.php?topic=5385.msg36008#msg36008