The ability to jump would improve the game tremendously in a number of ways.
1. Combat could be made more interesting. The ability to swing in mid-air, have actual air-specific combos, and even have weapons that perform better in mid-flight would make battles and equipment feel more engaging and complex. Flying monsters could be made that must be engaged in flight.
2. Similarly, monsters with certain attacks could be avoided by jumping. Imagine jumping over a Trojan's horizontal sweep, or over the ground spike attacks created by large red lichens. Perhaps an earthquake will stun you if you don't time it properly and jump before it hits.
3. Puzzles could be made more interesting and levels more 3D and complex if gravity were a factor. Even something as simple as jumping from moving platform to platform over a spike pit could be fun.
4. Small spikes traps could be leaped over, giving the player more maneuverability.
5. A new equipment slot like boots could govern factors like the height of the jump, the horizontal distance that can be covered, and the speed of the descent (like temporary hover-boots)
Of course, there would have to be some limiting factors to avoid Jump becoming something you do all the time, any time. A couple of ideas:
1. Movement speed is slowed down in air. This should make it difficult to simply jump over and avoid pit spikes completely.
2. Perhaps it should be impossible to shield in mid-flight, or have reduced effectiveness / shield health while jumping.
3. Things like elemental traps and Vanaduke's lava shouldn't be jumpable. This makes it so there can still be movement barriers without making them enormous.
4. Not all weapons would be as strong in air as they are on the ground.
I can really imagine jumping making the game much more enjoyable. Problems like rooms with rising or falling lava / acid levels could be epic.
It might be possible to make Jumping a limited action in certain scenarios, such as specific levels where jumping is enabled by a pickup and lost upon exit by the elevator. This would allow for adding Jumping to the game as an incremental addition rather than a tremendous game-rocking patch.
Otherwise this would certainly require an overhaul of all existing gate levels.