Without that you pretty much just have an interactive game with no interactivity, which isn't very useful.
Where one man sees a desert, other sees a bunch of sand. Also, if an entity has no interactivity, it is not interactive anymore.
Regarding the functionality, the SDK is a perfectly suitable tool to implement any API that is in the mind of a game designer, no need to have that implemented just for a headless exporter. Actually, i vote for a totally different approach; the logic is one part, the renderer other, the sdk with plugins the third, and by skimming the source of the c2 engine for the last two years, it doesn't seem impossible.
It's cool, a close approximation of a headless exporter is achieved with exporting through nw, hiding a window and using it as a silent exe/other format, and communicating with it with any kind of preferred way. Some of the multiplayer stuff i did is hosted that way and it works, a working http/socket.io/udp server written in c2 is already deployed an live and accessible through a public ip/url . But it's hacky, we have to have all of the nw juice to get it running and it makes scaling a lot more difficult and a lot of computing resources for stuff not required.
I'm kinda sad you don't seem to see a wider picture here, games are not just what a player sees, games are multiple systems behind the game. Having c2 exporting pure logic will be beneficial for all kinds of aspect for a game dev. Also, i must say i'm making this request as a game dev, not a software guy trying to do non-gaming stuff with c2.
Although, again, i'm surprised you don't see benefits of a headless exporter would bring to the gaming aspect of developing possibilities with c2.
tl:dr; this is not a priority request, and is doable with current stack, but...