He doesn't even seem closed off, though. There's a lot of "tell" involved, not least in the way Rose heals Nine when from the looks of it that's the result of accidental and later less-accidental meetings with the demons in his head. Jabe is the one who catharts him on the death of Gallifrey, the Daleks taunt him into refusing to see himself as a killer. Rose doesn't even necessarily know what he's done, let alone talks to him about it.

As for Ten... when it's not telling us how much he needs Rose he's fine with wandering off and he builds deep relationship fast with other people. If she'd left at Christmas or with Mickey he'd have felt wistfully sad for a week and then moved on safe in the knowledge that she was fine and happy and with cheery memories of their time together.

In conclusion, the very worst thing Rose Tyler could have done is refuse to leave the Doctor voluntarily. The seond-worst thing would be to refuse to let him have another friend around just on the off chance that something happened to her.