>If the suspect had a file named "Not evidence of me stealing my neighbor's safe" and "Definitely not a video of me practicing how to break open a safe" would it be fair to assume the warrant doesn't allow access to it?
No, this is silly. That's not how search warrants ever work. The Fourth Amendment imposes no such "only search where labeled" requirement. It does, however, mean that police can only search areas where they are likely to find evidence of the commission of the crime that is alleged in the affidavit. For example, if the crime is theft of a full-size refrigerator and police have probable cause to believe that the stolen refrigerator is located at the residence of the accused, they can go into his house and look for the refrigerator anywhere that a refrigerator could be. That does not, however, given them the right to go rifling through his file cabinet or his underwear drawer, unless they have specific, articulable facts (i.e., not just a hunch) that there is probable cause that some other evidence of the commission of that crime will be found in such places.
What does that look like when searching a suspect's cell phone? Obviously every case is going to be different, but the point is that warrants cannot be utterly boundless. Such "general warrants" are one of the reasons the American colonists listed as a grievance against King George in the Declaration of Independence and today issuing such warrants would be considered prosecutable malfeasance in office. if police want to use search warrants as evidence-gathering tools they have to follow the law or convince the legislature to change it.
EDIT: Actually, consider this as an example.
California Penal Code § 653m says the following (subsection b): "Every person who, with intent to annoy or harass, makes repeated telephone calls or makes repeated contact by means of an electronic communication device, or makes any combination of calls or contact, to another person is, whether or not conversation ensues from making the telephone call or contact by means of an electronic communication device, guilty of a misdemeanor. Nothing in this subdivision shall apply to telephone calls or electronic contacts made in good faith or during the ordinary course and scope of business."
So let's say jilted boyfriend decides to ring up his ex-girlfriend a couple dozen times in the wee hours of the morning, but he uses something to block his caller ID. In that case, there might be evidence on his phone that he dialed the girlfriend's phone number when she claims the harassing phone calls came in. So can the police search his phone for evidence that he called her number? Absolutely. Can they look through everything on his phone (pictures, notes, settings, etc.)? Absolutely not.