Well, you can stab with a two-handed sword, and it's not ineffective. And, historically, a "dagger on the end of a long stick" isn't called a dagger, but a spear (or other polearm).
Sure, but it is still the size of a dagger, and has about the same penetrating force as a dagger. It just has reach. But when has a spear done as much maximum damage as a dagger in D&D, or a spear done as much damage as a two-handed sword? Never, which is dumb.
I wouldn't mind seeing this kind of weapon be good against large enemies, though. Spear for large game, lances (from horseback) for exceptionally large game (like dragons), etc. It seems to fit within a fantasy context rather well.
Bringing back the lance's ability to do double damage from the back of a horse during a charge would be a good start. Heck, bringing back the lance at all would be a good idea.
The downside is that it's fiddly. Easier way around that is just to say "bigger weapons deal more damage" as a general rule.
4e weapon qualities show a way to do weapons that is a fairly elegant compromise with simplicity and weapon design. It is just a shame that they kept differing weapon damage values.
If you classify weapons based on what they do, and give that class of weapons qualities which give them differing damage in different situations, I believe it is completely workable and simple.
And thus my take on bigger weapons with a bigger damage die. Yeah, you only need three inches of steel to kill a man, but push comes to shove, would you rather be hit by a dagger or two-handed sword? A well-placed hit from either is basically death, but a glancing blow or nick from the two-handed sword is certainly a lot worse than the dagger is. I've been nicked by a knife; I don't want the equivalent from a two-handed sword. As always, play what you like
The Romans scorned the Gauls and their use of a long slashing sword, believing it was only good for superficial glancing injuries. They put their faith in a short thrusting sword and a shield, and their record in battle against the Gauls speaks for itself. You wouldn't know it from D&D though, because a short sword always does less damage than a longsword or two-handed sword. If you were using D&D stats, the Romans would lose to the Gauls every time.
A two-handed sword has its uses. If you don't need a shield because you are wearing plate armour, it increases the reach and power of your longsword substantially. Good against calvary, good at cutting through swaths of pike formations. But there is a reason that he generally lost to men wielding an estoc or rapier.
The large two-handed sword is slower, has a large arc, and is difficult to recover from a missed blow. When a man overcommits with his large weapon, a man pretty much has his pick of where to stick his blade, as large portions of his body will be exposed by the errant swing. So a rapier doing half the damage of a two-handed sword in that situation is baloney.
Or how about the fact that nobody ever uses a dagger to backstab anyone? Really, assassinations are the reason a stiletto was created, but nobody ever uses them because they do less damage than a short sword or rapier (or pay the feat tax to backstab with an even larger weapon).
This can all be laid at the feet of differing damage for weapons, because the D&D community can't be convinced that weapons were designed for tactical advantage in specific situations, not because one weapon is superior to another.
There are ways in which weapons do more damage than other weapons, but they aren't absolute things. A club doesn't have as much mass as a mace, nor metal ridges or spikes designed to bend or pierce armour. But against an unarmoured opponent, a club does the job just as well. (This is why armour should be damage reduction instead of AC but that's a debate for another day).