Perhaps my grammer isn't as sharp as it should be, but I don't understand how "go in" would be any different. We say "please go in" and "please go into the room" without any issues, I think. What is fundamentally different between "sign in" and "go in" leading to this style guide not also discouraging "go into?"

I don't interpret a meaningful difference between "can not" and "cannot," nor between "any more" and "anymore;" thus, I don't find a meaningful difference between "in to" and "into."