I really like the Dust templating engine (
http://cretz.github.io/dust-php/). It has hints of Mustache and Twig.
One of my favorite things about it is the various types of $context it is able to interpret. You can pass it an array, a simple stdClass object, JSON object, or a class with methods. On top of that, it was first written as a JS templating language, and then ported to PHP, so it was built with client side rendering in mind. It would be easy to make the same layout markup work with both a web-services approach as well as with server-side rendering. I know the other templating engines do similar things, but Dust is the new kid on the block written by the Linkedin Team.
So, to answer your questions:
1) Pro: A template engine in core would serve as an example for extension / app devs to work from, which a lot of people (including myself) need. Con: PHP has pretty good html templating baked in (it IS what is was originally built for, after all)
2) I would say yes. I would like it to be able to use Dust or Mustache out of the box. I would also like it to be SUPER simple to add in more support for more engines, when new & improved versions come out.
3) See #2
4) I'm in.