The basic idea is to have a clear and pleasant-to-use web-based interface for generating a MediaWiki instance manifest. The interface should allow you to tick off the extensions you want, for example, and it would automate the configuration of supporting software like Apache and memcached. There's an attractive example of such an interface at https://puphpet.com/.
MediaWiki-Vagrant already implements the bulk of the work in that it provides a set of parametrized, MediaWiki-oriented Puppet modules and resource types. In plain English: MediaWiki-Vagrant can take a configuration file that says "give me a MediaWiki instance with Scribunto and VisualEditor that is set up for development work" and configure a machine to match these specifications.
A number of cloud computing platforms provide hooks for uploading Puppet code to automate the creation and customization of servers. Some are event implemented as Vagrant 'providers', which means that you can run 'vagrant up' and Vagrant will create a cloud instance rather than a VirtualBox VM. Examples include vagrant-rackspace for Rackspace Cloud (https://github.com/mitchellh/vagrant-rackspace) and vagrant-aws (https://github.com/mitchellh/vagrant-aws) for Amazon AWS. A vagrant-openstack provider (https://github.com/aodn/vagrant-openstack) also exists; I don't know how much work it would take to make it work with Labs.
The major work-item would be to build the web interface (or adapting the source code of https://puphpet.com/ or some other project -- there are several), ideally as a MediaWiki extension so that we can offer the ability to provision a virtual server (either local or cloud-based) right on MediaWiki.org.
I think that this could considerably broaden the appeal of MediaWiki to a new generation of internet users. The success of Wikia shows that there exists considerable demand for point-and-click wiki creation. It could also help drive third-party usage of VisualEditor / parsoid, if it is true that adoption is held back by anxiety over having to configure and maintain an additional software component.