To fly a light sport class aircraft in the US you do not have to have a current medical just a drivers license. It appears that many older US pilots have moved down from larger certified aircraft to LSA's for that very reason. However there have been
AFAIK no accidents in LSA's that are directly attributable to medical incapacitation.
Regulations are supposed to be evidence based. There is simply no evidence that not having the currently required medical for private aviation provides any appreciable increase in risk over not having one.