Do you really need HG/Livind Dead that early?
Maybe work out other strategies. And since it's that early in the fight, learn the mechanics first, then concentrate on optimizing for high dps.

The reason why they don't want to reset cooldowns has been explained as it could be exploited somehow. It hasn't been detailed more than that.

While it can be annoying, it gives you time to reflect and discuss what to do next attempt.

There is also a risk that cooldown reset on wipe leads to situations where you intentionally wipe because you didn't get the perfect opener.