It accomplishes many things that other frameworks don't, the most important of which are ease of use and dramatic productivity gains. I recommend reading meteor.com/about for a high level overview and then diving into the description of projects at meteor.com/projects to understand how the various components of Meteor function. The original screencast at meteor.com/screencast is also a very useful introduction, and if you want to spend about half an hour building an app to get the basics down, meteor.com/try will do just that.

Using phantomjs to index your site has not caused any problems for most of us building apps in production for the past two years. From an engineering standpoint there are better alternatives such as server-side rendering (btw, there is a Meteor package that does this: https://github.com/meteorhacks/meteor-ssr), so outside of performance considerations this isn't a super big deal. A lot of Meteor apps also aren't Google-facing but instead apps that you use after log in, where Meteor's advantages have the biggest effect on one's productivity.

Meteor works in every evergreen browser and quite a few older ones. It will fall back to polling if there is no support for websockets and the Blaze view library works in IE8+.

I recommend just trying it out. It takes no time to install and get your first app started (<1 min) and you will immediately start to see the benefits. Come tell us more about your situation at forums.meteor.com and maybe we can help!