Another problem, is I blame NCsoft. They should add some stat requirement before they can do a dungeon.

To be fair, setting some sort of stat requirement would just be another barrier to new players. Besides, your character stats has an infographic that suggests "what gear is effective in which dungeon", although all that is just a guideline.

Now if someone is going in with way below the bare minimum that's just blatant trolling, but devising a way to prevent that contains a lot of complications that can also negatively affect legit players.

when I was 500 AP, on my second run through Asura, a party of all 500 AP, we did not have enough DPS to kill Asura

The bare min AP for Sogun's Lament/Sundered Nexus is very much 500, perhaps lower; when they first came out (which was after Lair/Yeti/Necro, the easiest Silverfrost dungeons) majority of the playerbase was only armed with some Awakened/True Oathbreaker Weapon + True Siren/Awakened Oathbreaker Accessories + 8-piece Yeti Soul Shield, plus the game considers Nexus to be easier. If your party didn't have enough DPS on Asura, your party members probably have no idea how to perform their class rotations properly and/or are constantly dying. Asura literally hands you up to 800 AP just for doing mechanics properly, and that boost to 1.3k AP is more than enough to succeed him.

Yeti also had significantly higher HP on release (7.5 million) and the AP buff Yeti gives is negligible, yet 500 APs could still succeed 4-man. If Yeti can be defeated with that AP with 4 people then I don't see why 6 people with the same AP and the massive stat buffs can't defeat Asura (and by extension Heavenpiercer).