Eeeeeh the Traverse Town one doesn't count. He has the option to unlock it after he learns about the Keyblade from Yuffie and Leon. Not being able to unlock it (and the big safe) before then is justified by Sora not knowing what his weapon is yet.I have another nitpick.
This game has the tendency to forget something so completely obvious but plot and gameplay forbids them to remember. Like something as obvious and simple as a door being locked when you have a goddamn KEY that OPENS. ANY. LOCK. for a weapon.