The dream is definitely not trusting certs which haven't been written to a log. I think that the path is actually in sight too. The CAB forum seems relatively on board.
You can experience this dream today by simply installing Google's "Chrome" browser. If you prefer a different browser you probably don't have long to wait, Firefox and Safari have announced plans to check CT (Apple says in Calendar Year 2018 but I won't be astonished if that slips) and it's something Microsoft's browser team are contemplating - if you care about trust in the Web PKI you obviously shouldn't use Microsoft's products anyway, but if you do...