I use nylon hooklinks from 9" long (over gravel) to 18" long (over silt). I seem to catch enough carp on them. They don't tangle and I feel the carp find nylon difficult to eject.
Is there any point in me ever using a braided hooklink?
I don't think so...convince me!!!

Paddy, there are several uses for braid and I have caught 100's of carp on them.
a) over severe gravel eg. Harefield, Harrow etc it is less likely to chafe and snap.
b) because when it falls through the water it tends to coil unlike nylon, it can often result in better hookholds as by the time the fish tightens the hooklink to the lead it is moving away with a bait well in the mouth and then bolts as it feels the weight.
In the 1970's pre-hair days you always got more takes on braid than on nylon. Food for thought?