I have an attitude of 'horses for courses' with this. On a large Yorks / Derby SRT trip or deep alpine trip I take a dedicated shock cord. It's very useful for working yourself back up along 'challenging' rigging, and for derigging. Particularly when you have a 2nd jammer to put on your long cows tail.
It's not just super tight exploration rigging, but any time you have a very long hang above a rebelay, you should be putting in some point of attachment (i.e. long cows tail) to the bolt to stop you cross-loading your croll with the rope stretch which is bad both for your croll (ripping the front off) and the rigging (starts to shave the sheath), so that you simply pivot down with the rope stretch, then climb back up till level with the bolt, unclip & continue. You can do this with your shorts cows, but it can be a bit difficult to get it clipped in particularly if you don't have a Pantin, and leaves you rather trapped against the wall.
On a tight nasty little Yorkshire trip, I just do it French style (long cows as shock cord).
Personally my dedicated shock cord lives attached to my oval carabiner for my basic hand jammer (oval for easy hauling setup if necessary), most of the time stashed in my SRT bag. I usually just attach it to my braking carabiner for going up, with my descender then going in my SRT bag. My shock cord is in fact 'last years' cows tails, with the short cows chopped off after the sheath rubbed through on the barrel knot of the short.
I've seen people mess up the 'French' technique of just using your hand jammer.
It's not so much the dropping of the jammer, but of getting confused and loosing situational awareness. The big risk is that you unclip the long cows from your hand jammer when it is on the rope, to clip into a bolt etc., then unclip it again and assume that because your hand jammer is on the rope, you have a point of attachment there! I've seen people both prussic up a whole rebelay length with no connection between their hand jammer and harness, and also end up in a 'no point of attachment' situation at sloping ledge rebelays, walking their hand jammer up with nothing else on.