I'm certainly not sympathetic to the lawsuit, but I think I can understand why one would be lodged.
Of course I don't know anything about the family or their motivations, but had it been my son, I don't think I could continue on with life with just a "he did it to himself" response. I'd want to know if there was anything else, along the way, that might have prevented his death; I'd want to know exactly what happened that night. A lawsuit is probably the most objective way to attempt to get to the truth.
I also know that I would be angry. At him, at his friends for not taking his car keys, at the guy serving him more drinks, at the obstacle in the road, at the whole waste of it.
There are dram laws in MO, and I don't know that Shannon's is absolved by the offer of a cab because they continuously served him drinks for upwards of 3 hours. Hancock is a Big Boy, he could have turned down the drinks or switched to club soda. The servers and management at Shannon's are also adults; they should have abided by the dram laws and stopped serving an intoxicated patron. The laws are on the books because the same impairment that means a drinker shouldn't be driving will stop the drinker from having the sense to stop ordering drinks. Taking responsibility extends both to the drinker and to the commercial entity who knowingly made a bad situation worse.