DRK changes that would make it really fun to play

[Archwizard]

You have made TBN an offensive action now. By giving you a free Shadowbringer you save your own HP but also the healing from healers and all you have to do is make sure you TBN every 30 seconds.

So what makes TBN an offensive action here is that you're using it... to save your HP. Seems legit.

Even if I use Edge to mitigate the healing (depending on how many you need to heal yourself by 20%, let's assume 1), then technically, the Shadowbringer is not free, it has cost me 3000MP

And TBN already does every time you use it.
You literally are trying to have it both ways, each time you've spoken on this you've taken shots so broad they hit the existing TBN in the crossfire.

And, I cannot stress enough, I'm not saying "It'll be fine if they do exactly this." It's just a demonstration. I'm not gonna argue the specifics on a made-up example.

Also, point to a healer that would like to see a tank's HP yoyo around as they use their kit.

That's part and parcel with playing alongside any tank besides Paladin, at least since 6.1.
Warriors have lighter mitigation than other tanks but make up for it with self-healing. When a WAR takes big hits, we just shrug and say "Oh, he'll be fine." They're also... kind of the favorite tank right now.
When Gunbreaker uses their invuln, after the momentary heart attack, we shrug and throw a lazy HoT on them.
When Dark Knights want to use their invuln now, they pretty much stop using any mitigations and sink like a stone anyway. Sucks, but we're getting used to that.

So if you told me that DRK was able to self-heal from that occasional 20% hit due to supplemental changes to its kit, on top of it having above-average mitigation, and that I'd only have to panic if they did something incredibly dumb, I'd shrug like I would with WAR.
Is it a bit of a pitfall set for inexperienced players? Maybe, but only as much as being able to hardcast 5 second-long spells on RDM, or not being locked out of opposite element spells on BLM, or... half of the other jobs available. Knowing how to manage your own resources is part of mastering each job.