Many years ago when I was still in school, I had an old Honda that had a noisy water pump. On my way to the shop to get it changed out, the pump seized and fried the belt. I noticed the temp gauge literally shooting up. I shut it down and let it roll to a vacant parking lot, where I was able to call the shop and have a truck sent to get the car. I was only 1/2 mile from the shop when this happened, but the temp gauge was a clear indication I would not make it.
A few years later, I was driving a Buick 100 miles from home when the alternator bracket broke, throwing the serpentine belt that drove all the accessories, including the water pump. At the time, I was 3 miles from my sister's house. I found that if I let the car cool for 30 mins, I could drive 1.5 miles before the temp gauge would climb to dangerous territory. It took a bit more than an hour, but I made it to her house. Next morning, I found a replacement bracket at a junkyard and had it replaced with a new belt. Obviously the car had much bigger cooling capacity than the Honda.
I've also had 5 timing belt cars in my life. I still have 2 of them. None of them had a timing belt driven water pumps. 4 of them, 3 Toyota's and a Honda, have timing belts and allowed for the water pump to be removed without even removing the timing belt cover. The fifth one, a Mazda, required much more than the timing belt to be removed to get that water pump out. All the American cars I've had used timing chains.