I think it's a "always keep your cards close to your chest unless you absolutely trust them" kinda thing in this manga.
This argument only goes so far.
And when you are on an escort mission, I think letting them know that you have no stamina limit in terms of walking, is very much something that you are better of doing than not. For various reasons.
I do however agree that he might want to keep the "sp costs of skills is nulled too!" part semi-secret. Unless he wants to very much advertise his speciality as an escort adventurer, to get the higher-paying contracts. But even that possibility should not be relevant for quite some time yet (so not telling everyone about that part still makes sense either way), as he still needs actual experience, system-experience, and higher rank for more trust.
Yeah, but he was also kicked out of the castle for being appraised with the skill. Even if he's dumb/naive, he probably learned from that that people knowing his skill is probably not a good idea.
I forgot about that! I suppose he has absolute zero reason to not let ppl know about his skill (in its most basic function) then, as ppl already know he has
a skill named walking. And surely curious what it does (as someone else said, they even kept an investigation going on him), so saying it simply makes walking take no effort, without mentioning the other bonuses (leveling with steps, skill sp costs, etc.) would even possibly throw them off thinking that's all.