[Old habits die hard. The whole "walk behind me" nature he had a few years ago doesn't just vanish overnight, despite the growth of his character. Besides that, Katsuki has a lot on his mind...and he is in a bit of a hurry to treat his wounds then start gathering information and trying to figure a way out of this place. There's too many unknowns, too many factors to consider, too many "worst case scenarios" playing out in his head. He wants to have faith in his friends and classmates, all the other Heroes on the battlefield, but with the overpowering force of who they were up against...it's hard to hold onto that hope.

So yes, his pace is quick, even if it strains his body. He's not exactly focused on just himself right now.]

Mm? Tch, that goes for anyone if they have the fu--...fortitude to work hard. You got a goal? [He kicks a stone lazily with the toe of his boot.] Then fight for it. No one's gonna just hand it to you. And if they try, then it's not worth it. It's not something you earned. Goes for anything - work, studies, skills, talents...