My math is fine. Read more carefully. The critical hit argument (down in one hit) works fine if critical hits do double damage. A perfect crit drops a fighter with up to 16 hp.
I wasn't trying to belittle your maths skills, just trying to establish the real numbers involved here. Even if you are basing it on the Crit equalling double damage (which
is mathematically possible to fell a 15HP character with a sword!), you're still talking about a pretty slim chance (about 0.08%) of ever doing that, and like I say, this is just for an assumed
average fighter.
I admit that 13 hp would be the appropriate number for a first level fighter if I was dead set on him going down on the third hit. However, I'm not, and 13 hp has the disadvantage of not allowing enough design space for the other classes. Having fighters gain 3 hp/level, rogues and clerics 2, and wizards who gain just 1 hp/level just doesn't seem like enough of a benefit from leveling up to me. Obviously, YMMV. So I choose to err on the side of a slightly more durable fighter. Although I suppose 2, 3, and 4 might be reasonable (meaning a 14 hp 1st-level fighter), and since you can't actually roll a 13.5, that would mean my character would drop on the third hit about half the time. And he could be killed by a good crit from a longsword, even if you assume the [MAX(weapon) + d6] model for crits.
Well, the core problem here is in the method of characters gaining set HP per level, rather than rolling Hit dice types, which will also tend to levy out on averages over the course of several levels.
Going to your example, the only way you get 13 hp from [maxd10 + Con bonus] is if the fighter has a 16 or 17 CON. Which is very, very high. For the 14 CON fighter they talk about, the number is 12 hp. Which might be enough, but seems a bit low to me. The 10 CON fighter we've been discussing is dead on an average hit from a greatsword wielded by a STR 18 fighter - no crit necessary. That's a bit TOO lethal in my book.
I'm curious about the devastating psychological impact of having the HP total reduced from 13 to 12!

....but anyway, the min-maxing element of the game should be factored in.
The point is that by having starting Fighters start at, essentially, 10+con bonus HP, you actually do reach the most popular number of average sword blows to fell a Fighter - being 3 - according to the poll here. And it pretty much mathematically holds out through 10-13 too.
If a Great Sword (d12?) is utilized by a STR 18 (human max!), I'd imagine they could do a lot of damage! However, STR 18 ought to be pretty rare, and I'd probably impose a minimum strength to use a Great Sword too, incidentally. Even then, the average score in this instant would be 6.5 + 4 = 10.5 - only just about enough to fell an average starting level Fighter (10 HP), without any Con bonus. Should our proposed starting character face such an opponent, he'd be sensible to consider his options! However, such an opponent doesn't equate to the average Orc, does he?
The bigger issue with using HD creeps in over levels. If you let the character add his CON bonus to all rolls, the numbers go nuts. Similarly, the hit point discrepancy between the classes can grow to ludicrous extremes. Even if you assume average die rolls, there's a HUGE discrepancy between gaining 5-6 hp per level (the avg. of a d10) and gaining 2-3 (the average on a d4).
If a Wizard has a D4 Hit dice (av. 2.5 per level), this could be argued to be a bit low still - but then they aren't meant to be Fighters are they? I agree that some sort of cap to the number of HD possibly gained should be used, and can even see an argument for Wizards getting a slightly higher HD type to make the discrepancy with other classes less.
But if you have a HD+Con Bonus being applied over 10 levels, say, then the average L10 Fighter (D10) is going to have 55HP + Con bonus (0-40HP). This is not that devastating, especially considering that the more dice rolls you get, then more likely you are to approach the average score (exceptionally high or low scores get increasingly unlikely). An average L10 Wizard, by comparison, would get 25HP + Con bonus (again 0-40HP). If you let it escalate after this point then you'd certainly get huge problems, but this is where HP caps ought to take effect.
I'll also point out that we can all safely ignore the proliferation of high con scores by admitting that a high strength more than cancels a high con. That's only not true if the character benefits from his high con score repeatedly over many levels. Which I've already explained is bad for other reasons.
Mathematically, the proliferation of High Strength blows is difficult to calculate. It depends on how many fights the character has!