But if you've bought gap you get an extra few year's ownership for a very small sum. My gap is £170 for 10k payout on my car. If my car is a total loss at the end of next year I will get a payout which is 4-6k below purchase price. Gap will cover that for a real pittance (170 quid vs 4-6k) it is an absolute no brainer.
As for running in a car, that only takes a a few hundred miles and you have no idea how your second hand car has been treated. As for sorting out new car problems, that's what your warranty is for, you also get extra years "in warranty" by getiing a newer car.