I think what you actually proposing here is a way for safe mining with cheap solution. I doubt mining was ever supposed to be safe.
However, as this really is minesweeper, do you remember how one wins that old game? By flagging unsafe/mine rigged tiles.
How about an action performed on a tile (except cave walls) to reinforce it once it has been identified as one causing collapse. put some wood in it with few nails (nuggets) and it would create a 3 tile radius support. in case you mess up and reinforce wrong/safe tile (which in reality would probably weaken this place) you end up with fake mini support, giving you false feeling of safety

As for idea of rendering every cave wall a safe one, whoever came up with that, go back to kindergarten. Miner's job is a big boy (read: nutjob) job, only for hard headed individuals.