#delay flight

A booking is a contract. The Airline that you made the booking with abides by its side of the contract -- to get you from point A to point B of said contract. Although there is a departure time and arrival time, the airline is not capable to promise these times will not flex due to complications. If there is a complication, e.g. mechanical problem, bad weather, security threat, then the airline is still responsible to get you to point B, by any means necessary, which would include using other airlines to do so.

Now, say you have a separate booking. The delay of the first booking has now caused you to miss your second booking. The first contract is complete. Although you arrived later to point B, the airline did as per the contract and got you there. It could not and did not promise to get you there on time. In the eyes of the second booking, you missed your flight and voided your contract.  A new contract must be formed and that will involve another payment. The second booking loss a chance to fill your empty seat with a paid one and will charge your for that loss. Sometimes it can be a hefty price, but sometimes it can be a minimal fee.

Booking flights can be cheaper and airlines are aware of this. It isn't by any means "fair" that the first booking isn't responsible, but do remember that there are many ways to receive compensation for delay/cancelled flights, which could help you financially pay for change fees with the second booking. Compensation is usually given through customer relations so be prepared to pay out of pocket.