Everything has had SSI. In fact the way that the BBC used to make their web site in PERL on Apache used SSI for their "Most Read" section.
ESI is different... Edge Side rather than Server Side.
The benefit is that you don't need one server capable of doing everything. You can have a separate web service capable of returning the "Most Read" section on different technology, different machines, elsewhere on the network... and ESI will interleave the output of these web services at the edge of the network.
Varnish supports ESI, and as one of the main reasons to use Varnish is caching you can reasonably expect (and be correct) that Varnish will cache ESI sections.
So Varnish will receive a document, cache the whole of it, and use an entirely different cache policy on a section of it.
It's all swings and roundabouts. I just have a strong preference towards not making any part of the solution complex by trying to make it do anything more than it need do, especially when other layers can be added that do that specific thing (caching in this instance) better.
http://wiki.nginx.org/HttpSsiModule