As you said, these are all the pieces already. If what I'd figure is your question it's easy to answer:
"How much damage would I do if I fire for $Length time?"
$Length * $RoF = X rounds
X rounds * $damage = gunDamage
X rounds * $DOT% = avgDotAmount
DoTs are smart in this game, they all have their separate timers and can stack independently from one another. This makes the damage as intuitive as possible:
dotDamage = avgDotAmount * ticks(element)
totalDamage = (gunDamage + dotDamage) * multiplier(element)
As this was far too easy to answer, I can only assume your question would be like
"When can I stop firing, knowing that my DoTs will kill the enemy?"
To which the answer would be "Never, unless the target isn't currently affected, then keep firing."
To us human player at least; for all the data is there in the fountain of numbers that spew from the target you are perforating with bullets. Would we be perfect computers, we could see when a new dot starts ticking(it wouldn't have a previous tick before it) and thus know exactly how many ticks are left. Being human, all we can say is "it's on fire" or "it's not on fire." This makes knowing for SURE your target is going to die impossible, the best one could do is make a normal distribution graph(wiki) with the probabilities if your target will die.
If that's really what you'd want, I could run it through some model, but it's still gonna be a pretty useless graph. Input the specific gun and skills you're using, and you could get a graph with probabilities mapped vs dotDamage. Even if you could watch that while shooting things, you can only guess how much health your target has left.
If instead, and my final guess, the question would be "How much do I overkill?" that amounts to the same, as that is also "Amount of dotDamage still to be done."
There is absolutely no reason to, except for the challenge, farm Terramorphous on TVHM. All those getting better loot and all those theories are lies.
Terramorphous becomes easier on normal mode without the health and damage multipliers and it is recommended to farm him on normal mode.
The only reason to farm Terramorphous on TVHM is if you are looking for a real challenge.
Best Answer
It's probably for Min/Maxers or as Kotsu says, people who want to make the game harder.
I have noticed that sometimes I'll need to wound enemies and my attacks will slaughter them outright; if the badass bonuses were pushing my attacks from 2 hit kill to 1 hit kill I could potentially want that. It's pretty edge-case though, and all of the bonuses are only positive unless you're trying not to kill something or die more.
It could also be for Duels now that I think about it; it'd be rather rude to take on a "fair" level 10 duel but one of you is brand new with no badass bonuses to speak of and one of you has +crazy% of everything.