a useful site can show you what you need in 5 seconds while you may spend more on a crappy site and what if you open in new tabs search results, how will that be counted?
Time on site can reflect that you have a website that actually has information that people are looking for, which would mean in seo standards that you are on the road to success or if the time on site is very low than you don't have the information on your site that those visitors are looking for. From my understanding time on site and bounce rate go hand in hand. They both directly effect one another.