Ah I see, in English I think of "in" and "into" as being very similar, but it makes sense that "into" does imply something different, so in Polish the word needs to be "do" because it is more emphasizing the direction. Thanks!
"W + accusative" can also indicate a direction, but it's less common than "do + genitive". It's difficult to find a rule when to apply which one, as it sometimes depends on the verb and sometimes on the noun. But "w + genitive" definitely doesn't work.