One thing to remember is that Chainmail rules were used in a wargame, and then imported to be used in a proto-ttrpg, so the rules makes sense the most applied to the former, when a single strike is straight up a kill.
Keeping that in mind, as you also point out, daggers and hand axe have a very low chance to hit an armored opponent, while higher class weapon like two handed swords are arguably the best weapon by a large margin, speaking strictly about chance to hit the opponent.
The lowest class weapon to be kind of reliable is the Mace (Class 3), that if pitted against a 2h sword (Class 10) has a difference of 7 classes, so the mace wielder gets the choice of having first blow OR parry, not both. In this case, it's a gamble: since the 2h sword has higher chance of hitting, you could forgo first strike and parry, getting a counterblow in case of success; or maybe you could go "all in" attacking first...but if you miss, the 2h sword has an higher chance to strike without a parry reducing the roll.