The mats used in gyms and the padding used in sports uniforms are made up of soft substances. Why are rigid materials not used?

If rigid materials are used, a person falling on the mats will suffer great injury. While exercising or engaging in any sports activity, the person is having a considerable momentum. If s/he falls or slips, the momentum reduces to zero. The force exerted on the person’s body will depend on the rate of change of momentum, i.e. the time taken to come to rest. This time is large when the mats are soft (the force is small), and small when the mats are made of rigid material (the force is large).