Interesting debate this and I have mixed opinions.
I personally don't care if all my personal data is being reviewed by law enforcement how-ever I respect the onions of others who do (Whether I'm in the U.K. or U.S., all though definitely not countries plagued with corruption (Yes I know the U.K. and U.S. does have corruption, but it's not on such a scale as others) - but that's another debate for another time).
Either way, if you're suspected of something serious which requires your personal data being looked through on your 'cell' phone, then it shouldn't be too much of a problem getting a warrant, it just won't be an on the spot search through your phone, it'll be done at a later date (And the data won't be deleted because it'll be kept in a secure location).
In conclusion, I'd be happy to show my phone to law enforcement, and for those who don't, then it's your choice and unless you're suspected of something serious, then it won't be searched, if you are how-ever then they can just get a warrant by presenting their evidence of why you're suspected of something serious.