I agree with you here; spiders and surrounds play a major factor in RMS ratings. If you had a 4" heavy gauge voice coil but with the soft parts of an entry level sub, the RMS would be in the 200 watts range. All an assumption of course, I have yet to read the speaker cookbook.
The suspension indeed does play a role but the motor and coil are the most significant (thermally). The suspension can help keep things in check mechanically (exceeding mechanical limits) but as far as thermally, its role is less significant (unless super stiff). There are pros and cons when it comes to suspension setups. I personally don’t see a point in running super stiff suspensions on setups that are going to play music for enjoyment. Enclosures start getting big, the subs don’t play very low, and it can take a good amount of power to drive them depending on enclosure size and how stiff they are.