From the rules:
”3.5.1.3 Rollbar Padding. All roll cage tubing located wherever a driver may likely contact the tube in a crash—head, knees, elbows, etc.—must be padded with high-density (emphasis /me) rollbar padding.”
I believe this is where the 'hard' padding characteristic comes from. And the rule does specify "_rollbar_" padding, and NOT 'any other' padding, or pool noodles. I'll suggest bring a receipt for this purchase.
Also, your question reminds me of a previous discussion.
In sum: 'The rules say what they mean, and mean what they say.'
In general - other than the commentary entertainment - words that are included are there for a reason; they're not superfluous.
For me, as a layman, I'll just guess about the impact forces in a rollover or serious collision, and believe (until proven otherwise) pool noodles would be worthless to protect a head inside a helmet which is likely to crack at first serious impact. Plus the rest of my body parts.
I'll leave the actual reasoning to the professional.