Use a lock nut on a presta valve?
The advantage is that it's quicker and easier to get the tube out and tyre off, and you never have to deal with jammed nuts. 

IME the nut will be wedged unbelievably tight the one time you get a puncture at an inconvenient moment, and you'll end up breaking the valve (if you have pliers) or not being able to get at the hole (if you don't). The problem there is that you do the nut up firmly when the tube is inflated to 100psi, then it goes flat and without the air pressure "firmly" becomes "OMG".

The fix for that over-tight nut is obviously to inflate the tube. Which is fine if there's a wee hole somewhere away from the valve, but if the tube burst or you brought a spare tube instead of a patch kit you just have to somehow get the value out of the tyre. Which is surprisingly hard to do if the only tools you have to hand are whatever is on the side of the road.

Disadvantages of leaving it off: The nut is slightly useful if you have a flat-section rim drilled for Schrader values, in that it stops sand and muck getting in through the gap between the valve and the rim and rattling round in a hollow rim or causing punctures. Obviously this isn't an issue if your rim is drilled properly, and a better solution is to buy tubes with Schrader valves. 

The nut can make putting a loose tyre back on by holding the bead in place by the valve while you try to balance the bead around the rim so it doesn't blow off. But a properly fitting tyre doesn't do that. And you could carry one nut in your repair kit, rather than one on each wheel (a saving of at least half a gram!)

(edit) the nut has to be tight enough that it doesn't loosen when the tube is fully inflated, but not so tight that it's hard to undo when the tube is flat. But often when you tighten it with the tube flat, when you pump it up the nut turns out to be loose. So to get it right you need to let the air out of the tube, tighten the nut some more, then pump it back up. Possibly more than once. Or you can tighten it once the tube is inflated and hope for the best. In which case you can easily end up back at the start of this answer.

The other 99% of the time the nut does nothing harmful. Nothing very useful either. It's just there.

(edit) Note that the question is not "what are the advantages of using the nut" or even "how do you use the nut", it is specifically "advantages of not using the nut". I don't think "if you do this the nut works fine" is an advantage of leaving the nut off.