I really like the features that rubble as a game mechanic would bring: real landscaping, earthen / rubble-filled walls, rubble dams, etc.; and I thought I'd throw in my take at an argument for it.
It is true that by its very existence rubble interferes with all underground activities, but that isn't a bad thing. I don't think it's been properly phrased yet (at least in this thread), but the biggest contribution of rubble isn't "difficulty" per se, it's pacing.
The more time-consuming it is to carve underground rooms, the more important outdoor spaces are, especially initially. Early forts would need to rely much more on above ground, outdoor workshops and a wooden hut or two for a dormitory and dining hall.
Eventually, a fort's underground spaces are readied and the outdoor spaces are phased out. But of course, a fort that expands too quickly will spill out to the outside areas, where it is much more vulnerable.
Bearing in mind that all creatures that dig are subject to this pacing, proper sieges -- sappers included -- begin to make sense. Walls can be deconstructed, but rubble has to be dug like soil, and sappers wouldn't have the infrastructure to dig quickly or efficiently, so the dwarves have a fighting chance to intercept them; perhaps they could drop rubble over the walls to bury them in their own tunnels. If siegers can lob projectiles over the walls, it becomes doubly important to balance which activities take place outside so that when a siege comes and interrupts them, the fortress doesn't grind to a halt.
It then becomes all the more satisfying when the fortress is finally fully mature, and more-or-less all of its industries are situated comfortably underground.
This also has benefits when coupled with a similar pacing change to farming, but that's a whole other thing.
In short, a rubble mechanic would definitely change game-play, but I believe it would largely be for the better. That said, helping to emphasize the above ground aspects of DF is something, but it does seem to go hand-in-hand with sappers, and furthermore I haven't offered any specific implementations. And the implementation would indeed need to be unintrusive -- DF is obtuse enough as it is.