It doesn't make much sense to get rid of cookies alone, not when there are multiple ways of storing stuff in a user's browser, let alone for fingerprinting - http://samy.pl/evercookie/
Getting rid of cookies doesn't really help with privacy at this point and just wait until IPv6 becomes more widespread. Speaking of which, that EU requirement is totally stupid.
The author also makes the mistake of thinking that we need privacy protections only from the NSA or other global threats. That's not true, we also need privacy protections against local threats, such as your friendly local Internet provider, that can snoop in on your traffic and even inject their own content into the web pages served. I've seen this practice several times, especially on open wifi networks. TLS/SSL isn't relevant only for authentication security, but also for ensuring that the content you receive is the content that you asked for. It's also useful for preventing middle-men from seeing your traffic, such as your friendly network admin at the company you're working for.
For example if I open this web page with plain HTTP, a middle-man can see that I'm reading a rant on HTTP/2.0, instead of seeing just a connection to queue.acm.org. From this it can immediately build a useful profile for me, because only somebody with software engineering skills would know about HTTP, let alone read a rant on IETF's handling of version 2.0. It could also inject content, such as ads or a piece of Javascript that tracks my movement or whatever. So what's that line about "many HTTP applications have no need for [SSL]" doing in a rant lamenting on privacy?
HTTP/2.0 probably has flaws, but this article is a rant about privacy and I feel that it gets it wrong, as requiring encrypted connections is the thing that I personally like about HTTP/2.0 or SPDY. Having TLS/SSL everywhere would also make it more costly for the likes of NSA to do mass surveillance of user's traffic, so it would have benefits against global threats as well.