I hear about kids getting into bad situations all the time who are"good kids" and I'd rather be safe than sorry. When my other child is old enough to have a cell I will do the same.
I too used to be one of those parents who thought it was an invasion of privacy to go through someone's stuff child or not. Three separate events changed my mind.
First was a friend of mine who had a 14 year old son who was notified by police they found messages from a child preditor to their child.
Second was a 14 year old found dead of a drug overdose.
Third was a suicide pact between a 15 tear old girl and a 16 year old boy.
What did these three things have in common? All were "trustworthy" teens with parents who "respected" their privacy. All three also had texts in their phone that had their parents read them these tragedies could have been prevented. The latter two cases had newspaper articles with the parents stating they wished they would have paid more attention to their child's media devices.