I wouldn't call it a sacred cow, just a personal preference.
I would tend to think of the 1e approach to breath weapons of them doing damage equal to the hit points of the dragon a 'sacred cow', because for the longest time that is just how it was and people didn't really question it. And departing from it is more than a personal preference. Indeed, you could say that part of the reason that I'm comfortable slaying this sacred cow, is that pretty much everyone that has seriously considered this question has realized you had to depart from it and we are comfortable with butchering that cow because we've since realized that it wasn't good for the game.
I also don't think your approach makes the game better for me, but it works for you and that's great!
Here you are suggesting that this is all entirely subjective, and I don't agree. There might not be 'one true way', but there are definitely things that make the game better. When you say this or that "works for you", are you really thinking how it will work for you when you are a 9th level cleric in a real and tangible PC party, having played your character for three years of blood, sweat, tears and laughter? Or is this all abstract and a feeling about what you would like that is untested against the reality of actually playing a game?
Fortunately I have never played 1e that high level (or with UA), that sounds difficult to DM.
Yes. Hence the reason I've been in several threads looking back and trying put forward a theory based on what I knew then, and what I've learned since them. I'm on the edge of running high level 3e play, and I'm looking at 3e and wondering what it might be like had 1e been written better in the first place and had 3e been trying to invent high level play from a better place than it started. At the same time, I'm thinking about both what I did write 30 years ago, and what I just didn't understand. So these are the dragons I wish I had had, and which I wish would have been the templates for dragons going forward into new editions so that we would always have had dragons 'right' and they could have been a bigger or better part of our play of a game that has them right in the title.
However, if what you say is true, why are you so concerned about making her stronger? If a non-optimized party can take her down in 3-5 rounds, why all the fuss about taking her BW damage to 300? Or giving her the salient divine abilities? (she became officially a god as soon as 2e, if not sooner)
Because theory crafting at least, I think she's pretty well balanced as is and I don't need to inflate her further to try to impress anyone. The point of her numbers is not chiefly to produce an effect on you when you read the stat block, but to produce an effect on play. And I've said repeatedly that what I'm trying to get away from is the over reliance on offensive punch that inflicts and infects so many 1e AD&D designs, and too many D&D designs period. And I happen to think that that problem in part comes from a conscious or unconscious tendency to want to impress and that typically it is offense and not defense that we deem the more impressive and first reach toward when imagining spectacle because it is the more active and obvious component of play.
The more her damage increases, the more any encounter with Tiamat depends entirely on the circumstances of it and the more binary the outcomes are likely to be. The 1e Tiamat is the poster child of that, with a creature whose breath weapons would threaten many gods, but which can be easily permanently slain by a not too optimized party of 6th or 7th level characters. Who goes firsts and under what circumstances is the entirety of the fight, and it all depends on what you call "scheming better", which is really just applying your system mastery against a DM that allows monsters to be passive foes - often because he wants to remove the possibility that he's using his out of game knowledge against the PCs (in that he knows their scheme). When an encounter depends entirely on a scheme, it is ultimately cinematically and narratively unsatisfying, and the soul satisfaction (if there is any) is in the self-satisfaction you have in the scheme. But honestly, after 10 years of that sort of play, even that wears on you, because it's not actually all that clever. It's just applying the gaps in the rules, and the sort of leverage you can get from using ill-thought out mechanics to gain an absolute advantage in a particular situation. After a while, it's sort of like the experience I had playing Half-life II. At first you think you are being clever. But then you realize that all the clever things you are doing are simply what the designers intended you to do and its all a bit of an illusion.
If I up the damage on the dragon breath weapons too much, all the implication of that is simply, "Don't fight dragons on fair terms. Figure out a way to win where the dragon can't meaningfully interact with you, because you don't dare interact with it." If the dragon breath weapon does so much damage it might as well be infinite, which is the obvious implication of a question like "why all the fuss about taking her BW damage to 300" (If 300, why not 360? Why not 400? Why not 500?), then the result isn't more of a fight but less of one. The PC's will simply find some advantage that they have over Tiamat which is so great that it might as well be infinite and exploit that.
But the ultimate thing that makes that uninteresting is not merely that it isn't as clever as a typical player thinks it is, but that an decent GM holds back from responding in kind. No GM that wants to keep his players plays the game with as ruthless bloody mindedness as his players, because the GM has infinite resources. If you make the way to play what you call "timing", then you as a GM must give up using that "timing" yourself. After all, any DM can arrange to kill a sleeping PC with the greatest ease, yet DMs almost never are ruthless in exploiting the PC's vulnerabilities simply because they can't be. At some point making the game all about commando strikes either excludes the DM from playing the game he is running, or forces the game to depend on illusionism where the DM eases up when he's winning. The drow commandos smashing through the windows of the inn, only to become mysterious bumblers and unruthless if the dice go their way sort of thing.
I guess what I'm saying, and this probably is arrogant, is that I've played this game at high level and you haven't and I don't really believe you know what "works for you". Someone like Lanefan on the other hand, has been there, and while his answers are different ones than mine, at least I can understand why he's giving them. Where as your critique seems to be something like, "But red dragon breath weapons being bigger than black dragon breath weapons is a sacred cow! It's always been that way. It doesn't need a reason beyond that." Yes, I know that. But I'm saying that's not necessarily the best design.