It seems to be taken as an article of faith that allowing Dexterity to add to damage would automatically be overpowered "Because Dexterity adds to so much" but that got me thinking about how Strength, Dexterity, and AC are interrelated. So I put some numbers up on a spreadsheet to get to looking at them all at once. And I have come to two conclusions. One, Strength and Dexterity are both important stats for AC. The second - unless you are a light armor user, Strength is by far the more important.
First, the obvious - How does Dexterity add to AC. That's relatively simple, every 2 points of Dexterity adds one point to AC. This starts at -3 for 5 Dexterity (the lowest you can reasonably expect to start a PC at.) So obviously, you need some Dex if you're planning to make a character who will survive on the front lines.
Now, how does Strength play into this? Well, the relationship here is quite a bit more complex. The AC bonus that can be derived from Strength always starts at +0 (because not wearing armor doesn't give a penalty), and is tied to carrying capacity. For purposes of this discussion, I'm going to assume you don't want to carry an encumberance penalty on top of movement penalties for armor, and thus we'll reference the "Light Load" carrying capacity column. Thus, at a Strength of 5, you can carry 16 pounds. Assuming your class can wear any armor at all, This is enough for Leather armor, or a +2 AC bonus out of the gate. (If you can't, you're almost certainly a d6/poor BAB class and Dexterity-to-melee-damage isn't really a concern.)
Continuing to reference across, for light armor this means that the best AC return will be a chain shirt, requiring a mere 8 strength for a +4 to AC. Choosing to ignore the Agile property (Mostly because it's non-Core), Medium armor has the Breastplate at a strength of 9 and a +6. And Heavy armor gives the best return at 13 Strength, with full plate giving a +9.
Of course, the above argument has a serious issue - it assumes the only thing you're going to be doing with your carrying capacity is wearing armor. No weapon, no shield, no magical equipment, and no mundane equipment of any kind. Since it isn't really possible to function like that, for the sake of argument let's assume that you'll never want to wear more than half what you can carry as armor.
Doing that, the chain shirt effectively requires a Strength of 13. The Breastplate requires you to have a strength of 15, and Full Plate requires a whopping 18 strength.
So, now we have some numbers to compare.
13 Dex = +4
13 Str = +4
15 Dex = +5
15 Str = +6
18 Dex = +7
18 Str = +9
20 Dex = +8
20 Str = +9
Well, that's interesting. Looks like the overall effect of the stats is roughly equal up through the range where PCs exist. I didn't really look at shields since they seem to be out of favor at the moment, although that would probably tilt things in favor of even more strength for defense. Also, remember that these additive effects are mutually exclusive - the more AC derived from Strength, the less you're allowed to gain from Dexterity. Further, I just took the raw amount added - the game assumes a baseline AC of 10, and Dexterity (counting from 0) starts out behind Strength.
So which is more important if you want a high AC? Honestly, while they both have some meaning, Strength seems to give the better return for AC up through the 'sane' range.
Obviously, this doesn't look at anything else Dexterity does for you. It still adds to a number of key skills (as long as you're not wearing heavier armor) and of course to Reflex saves. On the other hand, Strength also adds to-hit and damage.
So which is "better?" After going through this....I'm really not sure. I'll leave that up to others to decide.