My personal experience with subwoofers dictates that every single subwoofer I've ever been exposed to, measured, or felt, vibrates the cabinet when playing --- IE - you put your hand on the outside of the sub box, you are going to know the sub is at work --- with the sole exception of dual opposed design. Horns do, bandpass do, even typical sealed subwoofer cabs do. By no means do I think the dual opposed design is the only proper subwoofer design - it is a good one, but just one of many 'proper' designs. I'm sure you understand this as well, so that's why I ask for the clarification on your statement.
While I agree with you that the subwoofer FR should not be changed by placing the sub on a isolation pad - if the cab's vibration is causing the floor, cabinets, shelves etc, in a home to vibrate at audible levels, then the isolation pad may have some function in helping to dampen those physical vibrations throughout the house. I do agree the isolation pad will do nothing to dampen or modify acoustic energy being dispersed by the subwoofer driver - it will only dampen the energy transferred directly from the sub cabinet to the wooden floor. I will say that transfer/vibration can be quite noticeable on a suspended wooden floor verses a basement with the same subwoofer. I've heard my caps in multiple rooms, and on a suspended wooden floor they are all the more tactile than on a concrete slab.
I popped into this thread to see what people thought about placing an isolation pad on top of a subwoofer to help eliminate physical vibration transmitting to a speaker sitting atop the subwoofer. In the case of my JTR ported Captivators they vibrate fiercely when given some power. The cab doesn't make a poorly built or improperly braced vibration noise, it is as sturdy a cabinet as I've ever been in contact with, but just the fact that an 18" high excursion driver is pumping back and forth makes vibrations physically shake the sub box. I'm on a concrete basement slab so I'm not worried about transmitting vibration down, but not sure if the vibration in the cab would affect speakers frequency response or sound characteristic if I set my speakers directly atop the subs. I understand that optimal placement might not be with the drivers for sub and mains in the same vertical plane - but I have measuring equipment with the omnimic and if it measure too poorly I'll buy L and R speaker stands. The reason this question has come up for me is that I typically have used tower speakers, but have recently been playing with eD and JTR high efficiency speakers which either need a stand, or to sit atop the subs to get to the proper listening height. At current I've just been setting them atop the subs with cheap foam spacer disks from home depot.