I value your game knowledge, but can't agree on this one.
1. HP burn doesn't stack, but it make solid 75k damage every turn. I will be more than happy to spare one debuffs slot for hp burn instead of poison. And he already have Drako, one of the best poisoner in game, so no point to seek for second one. But he doesn't have hp burn and Tyrant can fill that role.
2 His A1 will heal him for 50% of damage and that means huge heal, not just some silly grean numbers. With Warmasrer proc that is just almost instant full heal. He will take damage when he cast ally protection and that self heal is as important as the damage itself. Yes, he will heal only himself, but that will make Apo"s (or any other healer's job) way more bareable.
3. Well there is a reason Martyr is considered one of the top 3 champions. But 50% Ally Protection for 2 turns and 3 turns CD, paired with high base hp,self heal on A1 and other useful stuff in his kit make Tyrant easy choise for CB.Yes, Tyrant is not Martyr and when the OP pull Martyr he can swap them with ease. Until then there is no sense to pair them Here we have a saying: one little fish in basket is more vsluable than all the fishes in ocean.
And again, his 10‰ damage reduction from his passive is something of great value of itself. In first this may seems meh passive, but getting 10% less damage from every hit in next 20 - 30 rounds is just something that can't be ignored. It is just too good overall.
We can't just focus on the raw damage when we talk about CB. Champions like Jareg or Rearguarg Sergant are not used for their high damage output, but for their overall usefulness.
And the thing is that the OP have good spot for Tyrant in Draco, Longbeard, Rhazin, Apo composition.