Spoilers mainly for Leo's Route
Leo wanted to stay in Echo for a number of reasons. He refused because he's stubborn, which is why the best ending means you HAVE to break up with him. Chase HAS to move on to get out. Part of Echo's supernatural effects is a burden. A burden of guilt, of trauma, weighing you down and keeping you still. Leo was ironically one of the more affected ones by Sydney's death, not that anyone got off scott free. More to say that it seems Leo's trauma response was to tighten up the group, and refuse to let them go, to let it go, out of fear. Moving out of Echo is a change, a big one. Leo cant do change. Even after what happened, in basically every route he STILL doesn't move. His trauma response was perfect for the curse of Echo to feed off of, keeping him there. His only reason for staying wasn't just his family, that was more so an excuse.