If you have checked bags, it won’t work because your bags won’t get pulled in time if you pull the “we weren’t paying attention and didn’t hear the announcement scam” Also, if you miss your flight they don’t have to refund the remaining ticket so that is a sunk cost. Right now, most airlines have pretty liberal re-book policies so I would just see the cost difference. If you miss one leg and the trip is on the same reservation, they will cancel all the legs if it isn’t weather related or their fault for some reason.