Or they do a gravity turn to round off the corner, largely in the same manner as that one math problem you probably did in school that involved finding the fast

Or they do a gravity turn to round off the corner, largely in the same manner as that one math problem you probably did in school that involved finding the fastest path that includes running on the beach for some distance, then swimming at slower speed to a point in the water. Also, different rocket designs have different efficiencies at different outside pressures due to overexpansion or underexpansion of the exhaust plume. Kicking a rocket out of the atmosphere--or at least up to a lower pressure altitude--with a big gun first stage changes the requirements a bit for the second stage rocket engine. It's slightly more efficient. But the biggest advantage is that you aren't ever accelerating the fuel for the first stage along with the rest of the vehicle. The disadvantage is that you need a very long track if you don't want to reduce vehicle occupants to thin red paste with excessive acceleration. Also, you can evacuate the gun barrel and put one or more plasma windows at the end, so your initial acceleration doesn't have so much atmospheric drag.