Probably needed to anyway, longterm burning of coolant produces steam that then erodes the cylinder walls in pitting. You should see the look people give when you tell them that, then you get to show them the damage caused by doing it. They think of it as a minor problem (I just keep adding coolant, right?) until faced with the need for engine replacement.
You think it's doing it at startup only, the leak accumulates then to make a crappy start, but the leak is often still going while running. Just small enough it doesn't really show yet.