Setting up some form of logging (that they are fully informed of) that doesn't require daily intervention (and you have the already-demonstrated good sense not to obsess over, or probably even look at most of), but you can access when needed, is not necessarily bad.
One possible method would be get them a data-only SIM, install a SIP client on their phone, and run your own SIP service for them (and you) -- as a bonus, you can wind up cheaper (potentially as low as the operating costs of the server, with all calls and texts free, if you take advantage of the right offers, different routing for sending/receiving, voice/SMS, etc.) this way. I haven't done it, because it's really a bit of work to set it up and, then keep on top of what VoIP providers are offering what services free, but amortized over a whole family, it could be worthwhile -- and then logging is at your discretion.
Of course, if your kids know you're logging everything, they will inevitably route some comms other ways -- payphones (if they can find them), their friends' phones, social networking sites, etc., so it's still no good for helicopter parenting, but if you're concerned about e.g. teachers starting predatory relationships with them, it could have some value.
Disclaimer: I'm not a parent, don't want to be (yet, anyway), and haven't studied for it -- therefore I make no claim that my ideas about parenting are particularly good. They are pure speculation devoid of research or experience, and the only thing dumber than yelling at me because I'm obviously wrong would be following my suggestions.
Yeah, I know that's all possible, but I'm not going to do any of that. 1) I don't log or lock down their computer at all. It's in a common living space and they know the rules. They still make mistakes, though, and I help them through those. 2) I just don't have the time to do any of that. I can barely be bothered to check the "Parental Controls" box for their browser (mostly because I don't believe it will do any good, long-term). 3) Maintaining my own SIP network while I have a full-time job, multiple kids, as well as other important things going on? Forget about it.