Tbf, that'd probably take a rehaul of the game's evasion and DR systems. Not that such hasn't been suggested already since ARR.
Personally, I don't necessarily find an anti-synergy to be any less interesting than a synergy.Though we could still put a blind on mobs in dungeons and raid adds etc, that'd still be fun. But go against wanting TBN to break
Wanting a cooldown's duration to expire before your next TBN comes up is, in itself, a further consideration that other tanks don't have beyond basic issues of multiplicity (stacked CDs have additive gains to eHP but multiplicative and therefore wasteful gains to heal-efficiency on you). Such is, therefore, unique gameplay, even if not the very most exciting sort.
The same could be said for HW DRK and the anti-synergy of DA-DD and Low Blow/Reprisal, since you couldn't both dodge and parry and you needed parry procs for LBlow/Rep. When you DA-DDed, you were going for full personal defense, less utility. And that's fine, so long as the job is balanced mindful of those anti-synergies.
Here's a real knife's-edge hypothetical: Imagine if TBN counterattacked, a la Dreadspikes, while active. At that point, you'd want to mitigate TBN so it breaks as late as possible for more free damage... without pushing it for so long that it doesn't break. That level of risk might not seem commensurate to its reward under the present design (likely preferring that TBN instead give back a portion of MP equal half its % of shield consumed, or the like, if it doesn't fully break), but that's just food for thought.
I think removing TBN would be more a stylistic preference than anything "obvious", but sure. On the latter note, though, just keep in mind reactions to having two competing tools for doing the same thing. If they can be layered skillfully and choicefully ("I'm going to try to have my increased dodge chance [enemy miss chance] last for just long enough to deal with this special hit, and I'll have TBN ready to bust if it does hit me, before the next two seconds' worth of pack autos can finish me off, since that'll still be enough to break it," etc.), then it shouldn't be accused of bloat, but otherwise it may seem wasteful and unpolished.