So, I was just thinking. Although Eugene is not the most bright character (perhaps made deliberately so), I feel like the writers want to move forward.
I dont see the show running for 10+ seasons, and this is already season 5. If they want a conclusion to the story (which I think the writers want to do, as the comics are nowhere finished I believe).
Over the course of the next 3-4 seasons I think the group will move towards DC and towards the "cure". I dont think it will be a happy ending, perhaps that there is a cure, so Rick etc. might feel they actually killed people instead of zombies.