"Estimate of weight and rigidity" is exactly the kind of thing that's performed rather well by low-dimensional sensing of actuators themselves.
Backdrivable actuators know how much current are they sinking - and thus, how much force are they facing. So even the simplest two finger gripper can easily "know" that one object is squishy and the other is not. The response curves are different. Same can apply to arm actuators for weight estimation.
Now, what this doesn't actually get you is an estimate of how hot/cold an object is, and how moist an object is.
Where cameras come in is specifically the "guide a grasp" part. Force sensing alone can tell a robot "the grasp is failing". A camera pointed at the grasped object can tell "why".
Backdrivable actuators know how much current are they sinking - and thus, how much force are they facing. So even the simplest two finger gripper can easily "know" that one object is squishy and the other is not. The response curves are different. Same can apply to arm actuators for weight estimation.
Now, what this doesn't actually get you is an estimate of how hot/cold an object is, and how moist an object is.
Where cameras come in is specifically the "guide a grasp" part. Force sensing alone can tell a robot "the grasp is failing". A camera pointed at the grasped object can tell "why".