Yes. Dust mites are responsible for many asthma related conditions and allergies and they obviously live in carpets and soft furnishings. Dust mites are significantly reduced by having wooden floors and are, therefore, ideal for asthma sufferers, as well as providing a far healthier environment. Rugs etc. can be washed or dry cleaned to kill any dust mites.
Dust mites are not visible to the naked eye but under a microscope they look like this:
Sanded wooden floors do not provide the environment to harbour dust mites and therefore provides a far healthier living area.