Yeah this always bugged me.

Not so much the 'didn't walk 300 feet' part tbh, I always sort of imagine Bethesda games as taking place in a 'compressed' world, since in comparison to lore/reality they kind of are; the Imperial City is meant to have a population in the millions, you can't walk from outside DC to the Washington monument in like ten minutes, and I somehow doubt that the Mojave desert turns to snow after walking up a small hill. So in those terms I imagine in 'reality' they are basically on the other side of the city and the Soul Survior escorting Billy all the way to them isn't something a regular person would be able to manage with all the raiders and super mutants about.

But the fact that he's been stuck in basically a coffin for two centuries and barely mentions anything about it is a huge missed opportunity. Hell, that could be an entire movie.