Firstly, the exception to due process during a traffic stop is based on the argument of a necessary expediency--that is, by the time the officer could obtain a warrant for the search, the car and/or illegal items will have been removed. The records of the calls and texts are stored permanently at the wireless carrier, so expediency doesn't apply (though the court seems to think otherwise about this at least in some cases).
Furthermore, the due process standards of a warrantless search are identical to those of a warranted search. In particular, the scope of a search is limited to its basis in probable cause. For example if an officer suspects a stolen cow in the back of a truck this does not provide a basis to search the glove box, or a locked suitcase found in the back, etc, although such searches can and often do uncover additional evidence in plain sight that form the basis to extend the search to new areas and containers. The same is true for a warranted search, again if searching for a cow in the back yard this does not provide basis to search a cabinet under the sink (or whatever).
In order to search a phone without a warrant the officer would need to have probable cause, i.e., evidence that suggests a possible link between the phone and the crime, for example if a witness testified that the suspect was seen using the phone during the act. Mere suspicion is not probable cause.