[Retric]

Suspension sits between a wheel and the vehicle so the entire wheel is displaced over a bump which means it’s momentum exaggerates a shock.

Deforming the wheel means far less mass is moved and thus momentum. This is why we use air filled rubber tires in the first place, but they have real size limits. So, this could actually provide a smoother ride.

Probably not worth it for a bike, but someone with a broken bone for example can be extremely sensitive to shocks.

[lolc]

The Loopwheels page is explicit about the wheels having a rigid rim.

[Retric]

Yea, but the wheel is more than just the rims. Play around here http://www.wheelbuilder.com/wheel-weight-calculator.html. The Rim is generally a large fraction of total wheel weight, but both spokes and Hub's are important.

On a bike the total weight also includes the fork and parts of the suspension. Not sure about wheelchairs, but I suspect deforming the center of the wheel still easily cuts unsprung mass in half.