But the bitcoin blockchain is already too big to store and sync on mobile devices with costly data connections - and it would only get bigger if it had to contain every SSL certificate ever issued!
You could have SSL clients connect to trusted nodes, like mobile bitcoin clients do [1], but then you've basically taken Certificate Authorities and replaced them with 'trusted nodes' so you're not much better off really.
The bitcoin blockchain doesn't need to contain every SSL certificate. It just needs to contain a SINGLE transaction conducted each day where the comment field contains the hash of a document published by the root authority. That document would be published elsewhere (on the site of the owner of the root certificate) -- the bitcoin blockchain would be used only to provide proof that the document hadn't been changed since it was published.
But the bitcoin blockchain is already too big to store and sync on mobile devices with costly data connections - and it would only get bigger if it had to contain every SSL certificate ever issued!
You could have SSL clients connect to trusted nodes, like mobile bitcoin clients do [1], but then you've basically taken Certificate Authorities and replaced them with 'trusted nodes' so you're not much better off really.
[1] https://en.bitcoin.it/wiki/Thin_Client_Security