SPDY doesn't provide a way to proxy-cache public assets, so it's bad for places that use such caching to mitigate low bandwidth / high latency connections.
http://bitsup.blogspot.com/2011/09/spdy-what-i-like-about-yo...
But yes, there remains no silver bullet, and you'll have to pick the right tool for the job.
Nothing stops a proxy from handling SPDY, if the client trusts it to do so and doesn't mind getting MITMed.
The authentication can happen external to the http or spdy transaction as well.
True, but insecure HTTP provides neither authentication nor encryption.
> if there is nothing sensitive about the content.
Encrypting only sensitive content leaks information to observers and attackers, namely when you transmit sensitive content, and which servers you connect to when you do so. Encrypting all content eliminates that information leak.
A SPDY client that trusts a particular proxy could easily allow that proxy to operate on its behalf, and SPDY would actually make that far more efficient.