Back in the day, I can recall captains making announcements to the effect of "We're just waiting for (#) passengers who are coming off a late-arriving flight from (X)." When the passengers boarded, the cabin cheered. This was back when the skies were friendlier. These days, I simply never book the earliest connection option unless it's the only option, or I'm prepared to take the risk. I've run through ORD, IAH and EWR enough times when I've allowed 3+ hours to connect, and was very grateful that I hadn't taken the risk!