All the way up to 60 you can kill green named with any melee, probably all light blue named as well. Dark blue named are either going to be super rare or impossible without serious twinking or 60 with uber gear. To put it into perspective, if the highest level mob in the dungeon is 10-20 levels below you, you could probably kill it. So basically look for dungeons that won't give you any experience or loot you would actually use.

You also have to consider things like getting to the named mob, pulling, FDing or running if it gets hairy. The only melees that excel at those aspects are gonna be the SK or a monk. Monk actually would probably be the best once its well geared, but without snare or casting interrupt it's going to be hit or miss. Well geared monk could probably even do some dark blue cons at great risk, but if you're looking for a mob by mob list by level, I'd say roll a monk and start making one. Not trying to be rude or anything, I just don't think a list of that nature exists and would be too in-depth to get all in one post on the forums. Maybe make a thread entitled "What named can a level 20 monk solo?" and explain the specific circumstances, that its not super twinked and would be dungeon named. Then after that thread, make one with "What named can a level 30 monk solo?" and so on. You'd probably still do better by rolling one, leveling a little, and taking on easy stuff, then working your way up.

Someone said bard but I have a 40 bard and have seen enough 50+ bards, so I have some real trouble believing they would do well at all. Sounds like corpse run city to me.

No melee is going to do well period soloing named mobs 30+ without some type of heals(fungi) or a friendly healer walking around outside of group healing. So which would be the least crappiest....i would say bard would last the longest before dying.

The entirety of all dungeon named in the game.

No one is arguing against the fact that a caster is going to be better at it. But if you were going to go with a 'melee' (and I don't really consider bards to be much melee, hell I bet Shaman are about on par with a bard for melee when using the right weapons) but bards do get the tools to do the job, albiet slowly if they're not just charming to win.

I didn't want a list just an opinion of which class would have the highest total

Bards have the best set of tools if your patient and prepared. I might be a little biased but I don't see any melee doing it better. But I'm on the fence about calling bard melee anyways

Within the confines you've presented monk but those are some pretty rough parameters. If you call shaman a partial melee (they tank a lot and swing their weapon while doing so) then shaman

Monk. Bards have lots of tricks but their low durability vs melee and ability to kill a mob in a reasonable amount of time (i.e. before something repops and kicks your ass) is absolutely laughable. Charm relies on mana which regens at 1 mana per tick, so that's only in the bag for so long, coupled with the fact that you're indoors (can't selos) and most named are in places where other mobs spawn/roam (not much room to maneuver). They are able to take fewer hits than literally every other melee in the game, and take them more often because of low defensive skills (I'm looking at you, Parry and Riposte).

Monk would have highest total. Outside of that, you're talking about greens and all the melees could kill pretty much an equal amount.

Bard really wouldn't be getting hit unless they fucked up, and nothing that some pausing for mez/regen can't fix.

I do agree its not fast. It is still more plausible for a bard than any other melee. Plus they don't need to be twinked. Give me some instruments and gtg.

If that were the case, bards would be camping dungeon named all the time. Can't say I've seen a bard camp anything named in a dungeon solo on this server even once, though that's not to say that it doesn't happen. At 60, are you able to kill lguk named like frenzy or ghoul AM?