I don't know, why you want to rewrite the whole PHP core? As far as i know, with PHP 7, a bunch of brilliant guys are working on it, right now! Nobody has to rely on one companies work, because this is an Open Source project and all developers out of the PHP universe can be a part of it. When you talk about hundreds of developers that support Gearman, RabbitMQ ... so this project, as of its PHP nature, has the potential to be supported by millions of PHP developers out there ;)
One of the advantages obviously IS, that it will be faster than ngix (Apache is too slow to really compare it) because it allows you to hold objects persistent in memory what no other web server actually can. So we have Magento running within the application server, and had awesome performance improvements around 50 % (means about 100 ms for a category page instead of 150 ms on nginx). As it is multithreaded (not forked) AND faster, it also allows you to handle more concurrent requests.
But that is only one thing, because a application server, beside the web server (what is only one component and maybe will run behing a nginx that delivers static content like pictures, CSS or JS), provides you with additionally services like a message queue or a time service that will be very helpful in nearly any bigger PHP project.
A very interesting thing will be to combine appserver.io and HHVM to improve performance. If this will be possible, we think it will make the servlet container part of appserver.io for sure the fastest webserver available.
As the appserver.io is completely written in PHP it allows you and any other PHP developer to help fixing bugs or to improve it by adding new enhancements like HTTP 2.0 protocol in the future. With such a big community, like the PHP community is, we can be much faster to improve appserver.io than waiting for Apache or nginx to came up with new features. These are the main reasons why we think that PHP community should have their own application server for PHP written in pure PHP.