That's part of the problem. Even if Strength had more going for it, though, it would still be ridiculous to use a puny rapier against a heavily-armored dragon or a death knight. The sword which people associate with that name is a weapon suited for dueling or civilian use, rather than the battlefield.
In that case, I will remind you that this is still Like Reality Unless Noted. Elves and dragons and magic can work however you want, because they aren't real and we have nothing to compare them against. A twelve-foot elf is exactly as realistic as a one-inch elf, and a dragon made of iron is exactly as realistic as one made out of leather.If your issue with how something D&D works can be summed up as "This wouldn't happen in real life!" I'll remind you that you are talking about fighting a dragon, something that also wouldn't happen in real life.
I hate the image of a rapier in the hand of Conan...or Elric...or King Arthur...or Aragon or...
They suck. There. I said it.
No, I hate the silly idea that you should be allowed to add your Dex bonus to melee attacks.
Meh, prior to 3e, that was called a Longsword. Unless you were using a two handed sword, there was no reason to ever not use a longsword. I mean, people are talking about the weapon vs armor table. Let's take a look shall we, just to refresh memory:
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So, a mace, vs AC 2 is +3 better than a longsword. And +2 vs AC 3. How often are you using full plate or plate mail armored foes? Virtually nothing in the game actually had AC's in that range. AND, virtually all magic weapons were longswords. Certainly all the best ones were. This myth that there was this magic time in the past where players chose a bunch of different weapons is just that, a myth. In AD&D, you used a longsword, full stop. There was just no reason not to use it. It was head and shoulders better than anything else.
It's no more silly than AC, HP, the stats themselves, adding muscle power to accuracy, the way speed works, most of the skills, turn based combat, healing, death saves, levels, or the rules for weapons.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.