Like I said, the links can be used to carry more gear, like extra rope (if you are wearing it as a survival necklace). I would not want to break a lanyard down for its rope, since its primary use is for carrying other things (each of which would have its own breakaway on my chain configuration). The rest I don’t really care to go back and forth on, because your discussion is getting pretty hypothetical.
Still, I have no problem with knots (other than them being cumbersome at times). But as far as the construction and practical purposes of breakaway lanyards go, I think a fused chain is fail-safe, multipurpose, comfortable (if not stylish), and simple to put together or repair with common items (usually one). So how is it easier to find more o-rings when they break? I can carry a lighter, tape, extra cord, etc., on my lanyard and it wouldn’t be an issue (although this could be overkill for daily use).
Your general rule of not cutting rope seems to be a technicality that is beyond the scope of this special case, in which breakability is the main requirement (while deconstructing the lanyard and reusing its relatively short rope for something other than carrying gear defeats the purpose of having one, especially when you could attach a more substantial amount of rope to it, as I was saying).
The critical concept here is that the chain is a redundant system, in which my having to reconnect it with a stronger binding (in a hurry) would not prevent the rest of it from working as a breakaway, and I don’t think this is over-engineering, because the links also function as points of attachment for various items, as well as distributing the impact of a breaking force over an area four-times broader than the cord itself (without adding bulkiness to the design). These may not be the attributes you want (and I am not saying that they have to be equalled by other examples), but they do have a purpose.