I delete my texts all the time and its because the phones don't hold that many texts. I don't think they are really trying to hide things from you. Kids just need there privacy. The reason you can't view what the messages say online is because its illegal. Sort of like opening someone else's mail. You can only get access to these messages through subpoena. But i don't really think its that big of an issue. Just keep in mind, when deciding what you are going to do, would you want someone viewing what you were saying?
Hope this helped.