I, personally, feel that if the police were allowed to search cell phones without a warrant that it would allow them to skip the trial by jury. Because, if we think about it, if we have incriminating evidence before a trial starts, the police can just say "Well, your phone says 'this'." Which, in my humble opinion would not allow the accused (key word, accused) a fair trial. Also, it could escalate to "Well, this was on your phone which we searched on the spot, so you're going to jail." If the officer has a warrant, then they have my permission to search my phone, lest they think I'm hiding something.
But, once you're arrested the police secure the phone, there is no evidence lost. They can get in front a judge quickly if needed and ask for a warrant. There is nothing stopping you from saying it's ok to search my phone, car, house, whatever.
Unless the police have reason to think that a crime is being committed or public safety is at risk, what harm is there in waiting for a warrant? I would be hard pressed to think of a situation where public safety would be at risk from a secure phone, nor could I think of a way a secure phone could be used to commit a crime. The police would still have the incriminating evidence before the trial, or do you think they could only get a warrant during a trial? So there is no harm in waiting, the evidence is still there, and your rights are protected.
After re-reading my post, I realize that I wasn't very clear, so that was my fault. What I was trying to say is that if the police can search our phones on the spot without a warrant, then it could lead to the trial being cut out (this is probably just my paranoia speaking, but still, stranger things have happened). We can also look at it from a another perspective and say that if the police were to search someone's phone without a warrant and they chose the wrong person (a law abiding citizen) that the person's personal correspondences could be at risk.
For example, I wouldn't want my parents going through my cell phone. Not because I have anything to hide (which I don't), but because it is an invasion of my privacy. Now, if I tell them they can go through it, that is a whole other story.
Well, you'd still have a trial, but they would most likely use that information to try and flip you into an informant.