I think seeing jumps in isolation can be exciting if the skater is doing something new, either that no one has ever done successfully in competition before, or even attempted, or that relatively few have done and this skater is joining the cutting edge.
As a competition for jumps alone, most jumps by most skaters will be just plain attempts, as high quality as the skater can achieve, but nothing more interesting than what they do in their programs -- if anything, less so.
So how to make it interesting?
The very best jumpers might attempt quads and quad combinations that have rarely been seen before. One advantage of having a competition phase for jumps in isolation would be that skaters don't have to worry about conserving their energy and stamina to get through a whole complicated program -- they just do the difficult jump, and then they rest before the next attempt.
But most skaters can't do lots of quads. Watching dozens of average seniors doing triple jumps in isolation would not be terribly exciting.
Would there be a way to encourage variety and creativity in jumping skills in a purely jump-oriented contest?
Inventing brand new jumps that no one has ever thought of before is not going to happen, especially not with multiple revolutions. There are only a limited number of edges to take off from (with or without toe assist for backward takeoffs), all have been attempted at least with half revolutions, and only the standard six takeoffs really lend themselves to multiple rotations.
And there are even fewer options which edges a skater can land on one foot and glide out on.
There are some known but rare/no-longer used skills that could become popular if rewards were built into the system. The potential of IJS is that if you give points for a skill, skaters will learn to perform it -- unless it proves physically impossible. The downside of IJS in terms of jump creativity is that if a skill is not listed in the scale of values and earns no points, few if any skaters are motivated to master it. And if the skill is defined in a way that would fill a jump slot but earn few points because it's difficult in other ways but can only be performed with low number of revolutions, or might be interpreted as a mistake, then the system actively discourages skaters from learning that skill.
So if there were to be a jumps-only competition, would we want to see that competition use rules that encourage takeoffs or in-air positions that can't be done as triples or in some cases even as doubles? Jump combinations with jumps other than toe loop or loop at the end? Rotations in both directions? Creative jump sequences that might permit a single step, edge change, or one-foot turn as the transition from one jump to the next?
Should there be room to reward creativity in air positions and in-air contortions (backflips and other acrobatic moves) that might require two-foot takeoffs and/or landings?
Or do we want the competition to remain focused on the same six multiple-revolution jumps we're used to, maybe with a few more quads?
In that case, the scope for creativity would be in the jump approach (into one of the six standard takeoffs), arm variations that don't impede and may assist quick rotation, and in what happens on the backward landing edge after (and assuming) it has been successfully established as a landing.
Within the current jump rules the quad axel is still to be sought, and there are still a few kinds of combinations that are possible and legal but have never or almost never been tried, e.g.,
triple flip or a quad toe or salchow at the end of a combination. But that's about it.
Is the goal to see many skaters trying to get as close as possible to textbook quality on the same relatively small repertoire of jumps?
Or is the goal to expand the vocabulary of jumping skills beyond just adding revolutions in the air?
Personally I favor the latter, but it would take a lot more rule changes to achieve it.
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For pairs, too. Eta: Synchro should really get in on this for on ice contortions.
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There's still hope for the silver fox. 
