you can :) in one of our local hacker communities (metalab.at) there is one guy who has written his webserver + homepage in C.
One of the major disadvantages that come to mind are missing shared data-structures.
And you actually would need to know what you're doing which reduces the likeliness once more.
Lets just say modern languages are much more comfortable to write such things.
As a "final" reason I would say to lowlevel for apps. if you're writing an App you actually don't want to write the engine, framework, server yourself unless you enjoy doing such a thing.