Use a lock nut on a presta valve?

I suspect a big part of the reason people leave them off is because it's something 'real cyclists' do- along with leaving off the dustcap, lining tyre logos up with valves etc. IME there are no real disadvantages to having them on apart from maybe a few seconds in changing tubes, which might get you some tutting on a group ride if people are hanging around waiting for you but that's about it. That said I don't use them on my road bike, and I do line my tyres up with my valves!

The main reason I don't use them is that they rattle when they come loose. If you're heavy handed when pumping though, the nut is useful.

Just remembered one other reason to use them... removing them if you've got a tubeless setup is a recipe for disaster

I prefer having the nut, because it makes pumping much easier, especially road side with a frame pump. I put them on finger tight and then retighten after inflating, and I've never had one jam, or rattle.

The nut is basically for ease of inflation when the tire is flat.

If you are a looks-oriented cyclist using one may make you look a little less serious, due to the implied fact that if you maintain your bike often you wont have flat tires from having your bike sit. If you have expensive wheels you might not want to use one for fear of it scratching the rim (cosmetic damage only, but still ...). Also, it is easier to take the tube out when you get a flat.

If you do decide to use one a little grease on the stem threads keeps it from getting stuck.

Some, especially little mobile, pumps do not have the tube and mount directly onto the valve which makes valve to move into all directions while pumping which is definitely not healthy for the place where your tube is connected to the valve. In fact I have managed to destroy a tube this way. The nut helps to avoid this problem by holding valve into the place.

Advantages of not using a lock nut: faster tube removal, looking 'pro', possibly avoiding damage to tube due to overtightened nut.

Disadvantage: I run big tires and deep section rims. If I try and push the pump head on to the presta valve, it likes to bury itself inside the rim to hide.

Keeping the nut on there stops the vaulve from going down in to the rim. This is important when I'm doing a roadside repair and using a small portable pump with a tight fitting rubber gasket. I've bent the delicate little valve on tubes due to poor purchase with the pump head, so I want this little nut holding things so I don't mess it up. I could push the back of the valve with my hands while I try to fit the pump head on, but this really sucks with some tires, especially the very puncture resistant ones which are not very flexible (panaracer ribmo) and make it hard to do this because they don't want to push down between the rim walls.

There is an advantage of the nut just being on the stem, simply because you know where to find it should you ever need it again. You will benefit from that helpful nut again if you have to take the tube off for whatever reason, and then put back the same one. For instance, patching that tube, or changing a spoke and nipple.

Now, some people believe there are certain risks, such as the nut becoming jammed (adding difficulty to tube removal), or contributing to valve damage in the event that the tire slips during hard braking, dragging the tube with it.

Whether real or not, you can eliminate the possibility of these risks by tightening the nut against the dust cap, rather than the rim, like in this image:

The valve has two different sized threads. There is a small diameter thread for the cap, and then a wider diameter for the nut. You only thread the nut onto the the second thread by just one or two turns. Lightly tighten the cap, and then turn the nut left slightly to add that little bit more tension.

Of course, in this position, the nut interferes with pump chucks, and so you have to completely remove it to inflate. But that only takes one or two turns since it is right on the end of the threads, a noted.

This might not be an intended reason, but it helped me.

Having an old road bike, the tyre clearance for 25mm tyres can be very slim. This results in "taller" tyre profiles rubbing against the top of the fork at the valve.

When I switched tubes to a valve with lock nut, I found that it "pulled" the tube around the valve towards the rim ever so slightly to remove this "bump" in the tyre, which eliminated tyre rubbing against the frame.

So a reason to have the locknut that I found useful is that it increased surface uniformity around the tyre

Not using that ring may save you some time when replacing the tube. Not using that ring may work out expensive.

I recently saw a video with a damage report on a velomobile, where the accident happened because the rear tire did blow out. The relevant part of this video starts around 12 minutes in.

The tire did blow out because the valve had gotten pushed in and gotten stuck against the tire's sidewall. A few seconds work with a nut/ring would have saved him $US.... (likely going up into the high 3 or low 4 digits) on his VM, needed to repair his cycle, or lowering his resale value.

I have used those rings on my bikes all my life, pump up your tire, tighten the ring and then undo it half a turn. That way it will never get stuck, it will have a very long way to travel to get off. And if you have the right size, it will not rattle.