Strategic bombers are just as important because MAD itself is fundamentally a political tool. The reason you have strategic bombers is, as you correctly said, so that you can signal your posture and intent by stationing them, dispersing them, launching them, and (most critically) recalling them.

Again, because MAD first and foremost is a deterrent, you want to provide offramps for both you and your adversary. Putting the B-52s on airborne alert sends a very strong message, but so does recalling them from airborne alert.

By their very natures, SSBNs and ICBMs are not capable of playing this role.