Both DDs have had lap tops in their bedrooms since they were 11, DD2 since she was 6.
To me it's a total non issue, You either trust your children or you don't.
I'm a very firm believer in giving children freedom as young as you can. Young DCs are far more likely to obey the rules than older DCs. By the time they are rebellious teens, the rules are already second nature.
They are used to me wandering in and looking over their shoulders and seeing what they are up to, they happily leave their lap tops on and lying about so I can read their history and their emails. I don't but I could.
I did used to read emails, mainly because DD1 forgot to check hers and DD2 had a DF with no security on her PC, who was the source of a whole lot of spam.
They don't have FB as DD1 didn't want it (and I'm not convinced its a force for good) and DD2 isn't 13.
This will change this winter as DD1's hobby are moving to FB from their Email list for planning events and DD2 will become a teen (yikes). However, because she's done a year at secondary I have a fair idea that her new mates are pretty sensible and am far happier than I would have been at primary.
Her primary friends were lovely, and many are still her friends, but some did tend to gossip without thinking who might read their kik messages and emails.