It's called "implied consent". You have to agree to submit to a breathalyzer when driving in order to get your license. All states use this type of law for breathalyzer among other things.
My point being, if you can be made to agree to submit to a breathalyzer when driving before you get a license, why can't you be made to agree to submit to this text-analyzer when driving before you get a license? I'm not saying this would be a good thing, but they seem very similar to me.
Implied consent still generally (up to your state) requires reasonable suspicion. It would likely be unconstitutional to have an implied consent law to search your trunk (or your phone).
The breathalyzer has the immediacy requirement described elsewhere in this thread, which doesn't apply to your phone. The only reason to avoid getting a warrant is convenience.