I've seen various engines do tunnels like this, and it does indeed strike me as a pain when it comes to custom map making. The idea of 'removing' patches in the terrain and filling it in with a model is an old one, and has been used in engines to this day. This would work fine for tunnels, seeing as that's pretty much a metaphore for tunnels in real life, however i think for caves it could be handled differently.
Since halo is pretty much all 3ds max, theres no real terrain in the game, just all 3d models, however in Unreal, one would use this technique of filling in the hole in the terrain with a model that resembles the terrain and inevitably leads into a cave. The entirety of the cave would be custom modeled, or a combination of various rock meshes thrown together to look like an enclosed area. In Half Life and Source powered games, this is all handled a little different, i believe the Terrain is generally handled as bsp. You can take blocks of bsp and convert them into an editable mesh, and people have used that for everything from curved walls to destroyed looking bridges, and of course, caves and tunnels. I personally have no expierience with Cry Engine, so i can't say if it handles it differently.
In short i don't think theres a single engine at the moment that has the capability to making it's own cave, and on another note, what if one were to make a cave or tunnel under water, how would the engine know to place an air bubble down there? Surely somebody will inevitably want to make "Rapture."
As far as ideas to solutions, perhaps if you took some of these heightmaps and applied them to a cylindrical mesh. This could work, perhaps, untill it gets to branching tunnels apart..
Perhaps you could take vectored paths, generate cylinders around them, and then apply height maps to the insides of those. It'd have to use some kind of means of knowing how to unwrap itself i'd suppose, but being an artist, i'm just tossing out ideas, i've little expierience as to the tech that would have to be implimented behind this. I can keep going if you think it's getting somewhere though, i love learning more about the limitations of programming, it helps me gear art more towards being a little more programmer friendly, haha.