In my humble opinion, as much as I like 5e and its game balance, I wish the weapons table was a bit better designed. It is not easy for players to choose a weapon for flavor or style/concept, when some are clearly more efficient. I wish some choices were a bit more viable. What if a Fighter has the concept of dual-wielding daggers? If the all-around weak daggers had a compensating perk in 5e, it could be less of a sacrifice to make that choice (which probably no one does with current weapons stats).
In this case though 1d12 is not bad at all, but why did WotC make the greatsword have a better average damage ? 5e broke from the traditions of past editions, except for the weapons table.
Anyhow, it probably won't change anytime soon.
This is where the DM comes in. I mean, WotC could
have put in a 3-5 page weapon table with dozens of different options. Or the DM could allow differently-flavored weapons: rapier flavored as a katana, shortswords flavored as daggers, etc.
Daggers are kind of balanced. They have weak damage, but are finesse, thrown, and
light. No other weapons are all 3, so you've traded damage for versatility.
And the greataxe is better if you want larger-valued crits and/or if you can reroll a single weapon damage die (not sure if this is a real mechanic anywhere)
As DM, I would have some homebrew, including revamping the weapons table.
About daggers having three weapon traits :
A fighter (or elves) would use two shortswords (like my Drow Wizard does in BG3) or two scimitars, both being light and finesse. The concept or style of dual-wielding daggers, for example, remains gimp. I used the dagger as a main weapon for a Gnome cleric with high-Dex because of lack of access to Martial weapons, and my party members thought it was a weak choice (in reality, the probability of hitting and average damage was higher than some other weapons due to Finesse). So, all in all, daggers are good for characters who only have access to Simple weapons and have higher Dex. Otherwise, players will not use them.
Players will naturally choose the weapons that offer better stats, which does limit conceptual choices, though yes the DM can modify the Weapons table.
A solution is to offer good magical daggers in the adventure. In BG3, for example, my Astarion uses a dagger that gives Bless one turn when it hits!