I don't think it will mean the end of shirt logos. I think it could mean there will be both options.
I'd guess a majority of shirt buyers are younger people who want the exact same one as the players - logo and all, so those will never disappear.
The Man Us of this world play to different sponsorship rules (although I'm sure they'd be delighted to offer different sponsors a space on their collar, and sleeve and shorts every week for large fee), but I'm sure they would find a way to monetize it too.