The issue with this is that rigid body physics (what's in use right now), is really super easy and most of the time that gets wasted by the processor is probably wasted on figuring out how static collision meshes interact. In other words, it doesn't require any sort of fancy hardware or math to make it happen.
Soft body physics is still perfectly doable, but it's a fair bit more complicated, there are less good, pre-existing, re-usable implementations of it, and it would definitely break physics compatibility in a significant way. That could be dealt with by making it an optional feature, but I've never heard good things about trying to make two separate physics engines work together to make something coherent. And modifying the existing physics engine, which is utterly about rigid-body mechanics into also doing soft-body mechanics...
In short, this suggestion is not easy to implement. It's also a pretty minor effect, compared to a lot of things that are probably easier to implement and would be more generally usable. I wouldn't mind seeing it, but I feel like we'd see a lot of other nice features first before this gets put on the table.
Practically, perhaps supporting joint additions in modding would be more useful, all in all.