I think it's finally dawned on me. Let's say (hypothetically of course) that I fitted a 16T freewheel to the other side of a flip-flop hub for a rider who is absolutely no relation to me and never intends to use it anyway, unless one of his legs falls off towards the end of the Dun Run.
This is a good quality Shimano freewheel - not your £3 Halfrauds jobbie - and yet it still has the characteristic wobble when freewheeling that every other freewheel and freehub ever made shows. This, I think, is why even a new track chain runs quietly on a freewheel - that slop means it's moving to engage the chain smoothly. A fixed cog cannot move at all - it's screwed tight against the shoulder of the hub threads - so it needs to wear into the chain, and vice-versa. Perfect chainline helps, but the freewheel is always going to be quieter with new components.
Is this a design feature or serendipity? Who knows.