The TPS62140's 30ns propagation delay is not enough to blow a fuse. The first rule of fuses (which many modern engineers do not understand!), is that fuses are not there to save your parts, and they simply will not do that. Fuses exist to prevent fires.

Even a fast fuse is very, very slow compared to semiconductors. I've seen transistors blow up to "protect" fuses. They're for stopping fires and preventing the slaughtering of batteries, nothing more, nothing less.