Superdragons and their sickass fire breath are not unbalanced. All it means is that, OMG, once in a while a tamer WILL kill you, whether you realized you were about to die or not.
Mages can do the same thing to you, especially necromages.The only difference here is that some players are high on themselves because they feel ultra-skilled on their mages and necromages. They think that they, as a class, are the only ones who deserve to be able to solidly kill someone now and then because they possess this special quality they call "PVP SKILL". They claim that "tamers" do not have this and therefore the class should not have this ability.
When's the last time someone thought they had gotten away, only to be leveled by that last, long-delayed explosion spell from that mage? The superdragon's fire breath is a bit like this, except that the tamer can't directly control when that fire breath is going to happen, they have to just keep trying to make things work out.
If you wish to discuss actual, demonstrable class quirks, we could take note that there are some templates that CAN NOT be killed by archers - - I suspect this to be intentional however, intended as a paper-rock-scissors type of deal in the design.
At some point in the past I asked the question - were tamers really intended to be a PVP class? The answers to that question are, if the answer is no, then pets' ability to attack other people should be removed entirely. If yes, then the class needs to be competitive at it. It would seem that the UO Dev people chose #2 and some of the people who primarily use other classes are not happy with the result.
As far as I'm concerned, the mage and necromage peeps who are so in love with their mage dueling skills are welcome to remain that way, but there's no harm in those guys having to watch their asses around a tamer and his superdragon when screwing around in the field in Fel.
Things would have been overkill with the old petball behavior and ninja tamers in animal form. The old behavior would have allowed a superdragon to repeatedly be insta-teleported onto someone while being chased down at mounted speed. But that's gone now and the pet has to move and attack at it's natural movement speed (which yes sometimes includes an initial warp at the beginning of the attack, a thing I don't find overpowering even when it happens to me).