Majority of HTTPS traffic is sniffable and largely non-confidential, unless you pad every file and web-request to several gigabytes in size.
Does your website use gzip? Good, now padding won't help you either, — unless it is way bigger than original content. Oh, and make sure, that you defend against timing attacks as well! Passive sniffers totally won't identify specific webpage based on it's generation time, will they?!
As for authenticity… Surely, you are going to use certificate pinning (which is already removed from Google Chrome for political reasons). And personally sue certificate issuer, when Certificate Transparency logs reveal, that one of Let's Encrypt employees sold a bunch of private keys to third parties. Of course, that won't protect authenticity, but at least, you will avenge it, right?
SSL-protected HTTP is just barely ahead of unencrypted HTTP in terms of transport-level security. But it is being sold as golden bullet, and people like you are the ones to blame.
I bet the SNI issues will eventually be fixed too.
And yes, with momentum behind certificate transparency, it could definitely hold CAs to the fire :)
TLS is no silver bullet, but it's a good base layer to always add.