As for shockwave for Vanguards - it could be viable, but not in it's current state.
I'd propose the following changes to it:
a. it should cost certain amount of barriers instead of having a cooldown - i. e. use a mechanic similar to the Phase Disruptor one;
b. it should have a sectoral (aka angular) distribution pattern instead of current linear one;
c. it should be way more powerful. ME2 level would pass;
d. it could both prime the targets for biotic explosions and trigger the latter.
e. another option - it could lift the targets (except for armored ones) and prime them.
I.e. - in the nutshell - could work like a directional biotic explosion.
Yes it needs improving. Most of the improvement could come from altering the geometry, which is actually a series of cones.
I am not in favor of combo proliferation though, that is a major problem with ME3 such that it mostly reduces meaningful distinctions between the powers. Now if Shockwave was one of the very few powers that could actually detonate a biotic combo, that might just be decent.
Clearly the nova animation is too long and leaves you too vulnerable to damage in cqc especially with full-on nova shield depletion right after a charge. Vanguard is unlike any other class in that your barrier will be gone 50% of the time or more during cool-down - you either Nova or Combat Roll or your dead. You can't even nova if your shields are too depleted. You might see implementation of I-frames as poor design and an exploit but it still requires skill and situational awareness to manage the barrier and cooldown mechanics in active combat. It's balanced and it's exhilarating fun so on some level it works.
In return for depleted shields bypassing the cooldown is a fair trade-off imo. Nova has always felt like it should be a Melee ability to me anyway which would bypass cool-down entirely under the present system. ME3 multiplayer version of shockwave is pretty great on the human adept I would put it on par with Throw and I wouldn't change much of anything about it because the range, width and explosion damage feels about right to me. Rather than remake the power to fit the vanguard class I'd rather they just kept it as it was for the adept and give the vanguard biotic slash instead and tailor that to vanguard.
I agree that the nova animation is overly long and idiotic, but I disagree that you need 1.5s of i-frame per Nova in the current form or state of the game, especially when Half Blast exists and Charge cooldown is basically the same length as total i-frames at 200% PRS (3.08s on HV). Nevermind that Charge is granting 50% DR for 3s 4s.
There is hardly ever a reason not to Nova directly post Charge, except when you can't Charge again afterwards. Practically the worst that can happen is that something staggers you out of the Nova during I-frame.
Disagree on current iteration of Shockwave. Besides the geometry being ******-poor, it has evolutions that do not work (at best), and others that are superfluous. It is only marginally better than Throw if you can manage to get two primed targets near each other, without any other targets in the way to waste the minuscule target cap (2). But given that it has short range and twice the cooldown, you would hope that it offered some advantage over Throw in at least a couple situations.