If it's a connecting flight, and the incoming flight is running late, then the airline "sorts you out". Basically they know sboit your connection and make a plan.

I've been on a plane out of Heathrow that waited for a 30-min late incoming flight. I've also been on a late flight where my connection has been rebooked for me because we arrived late.

If you book "2 tickets" you're basically a no-show to the first flight, and you're on your own dealing with that airline.