First, let's consider that if dash HK is not cancelable at all anymore, or is only cancelable on hit, the followup from qcb+P is made much, much less worth using, as you'll get punished to hell for trying this to get in. This is one of Vegeta's only other ways to get in on his opponents however, which is what he wants to do; otherwise, he's just using instant airdashes + normals, which aren't exactly unpredictable in any way.

Jump canceling dash HK at all really isn't a necessary addition as the only -realistic- thing this allows you to do, without considering the insane pressure he gets with it that does not need to exist in this manner (and his current empty cancel) mind you (so that we're thinking about this realistically and practically), is to either combo into his air normals, such as j.HK, loop with it using air down-back-forward+P super (has to be done in the air to be able to be looped), or cause a hard knockdown, which is what dash HK does right now.

That's really not that much, when the empty cancel is gone.

Now, if you were to only make it special cancelable, what he -can- retain is the essence of his old crazy pressure using it, while giving it limits. Right now, counters are extremely strong, they completely take away certain options on block as -very rarely- are they able to be blocked (ex. the CPU blocking my counter as I countered his jab). Knowing this, any attempted "blockstring loops", such as dash HK into qcb+P and repeat will not work when they have bar. You'll get punished with a counter, leading to a knockdown, which is not where you want to be in a fighting game.

In other cases, such as with qcf/qcb+K, he has a great way to keep the pressure on you without making it completely insane, as dash HK into qcf/qcb+K has very easy to see holes. Wolverine Flip can be contested if he doesn't do the followups, and Wolverine Sweep (as well as Elbow) can be blocked. Both Wolverine Sweep and Elbow aren't cancelable, so he can't do a ton off of it if it does hit you. Dashing back after Wolverine Flip, or dashing back and using the Elbow, or just doing nothing after the dash. These are all a TON of options that he has, while all having holes and parts where they can be punished, especially if the opponent has bar for a counter. None of them are as crazy as his empty cancel/jump cancel mixups, yet he retains their essence this way.

As for fireballs, yes, that would be optimal, since I don't believe fireballs need to knock down...like at all. They already work so well as combo tools on the ground for SSJ Goku and Vegeta, Goku doesn't have a ton of use for them, but that's because it's his style. But with this, any "fireball juggle loops" will no longer work, or at least they shouldn't work I'd hope. It may need some fine tuning if not. But definitely take away knockdown fireballs.