Since the first Indiana Jones movie, a wrist loop dangles from almost every bullwhip.
Some people even order whips with a wrist loop (at extra charge), which originally are without. If you want a screen accurate Indy (or one of the other typical movie whips), the wrist loop is of course a necessary part of it.
Otherwise, I consider wrist loops as obsolete to awkward (with few exceptions).
On long whips, I see a loop as decoration only, not to be used. Put your hand through it and you cannot change hands during a single whip routine. If your whip really slips out of your hand (rarely happens), simply pick it up again. Very memorable was Peter Jack's reply to my question, why the wrist loop of my target bullwhip was that small: he replied it's no wrist loop at all, but just for hanging storage of the whip. Never put your hand through the loop of a whip when on horseback. The whip may get caught somewhere, pulling you off the saddle with high risk of injury. Better to lose the whip and search for it afterwards. Modern cowwhips are often colored, thus easier to find.
On very short whips, especially signal whips, the loop may be useful. Originally intended for dog sleigh races, these whips can be worn at the wrist, to have both hands free but quick access if necessary. On both-handed work with signalwhips or short blacksnakes, wrist loops may also be applicable. This depends on personal preference. Never cut a loop off, this will mutilate a whip! If the loop is interfering, shorten it with one or two simple knots. To keep the loop in shape, don't pull the knot tight and undo it after use of the whip.