I am not just referring to able bodied, able minded is important too, 1 month isnt that long and I am not saying lock them in a closet for a month as a test either, they can still leave there house if they are lonely, they just wont have a caretaker with them, that wasnt an actual test that would be implemented, it was meant to describe the kind of people capable of surviving after all the services are pulled, there would be no actual "test", you would just survive or die.
As for Steven Hawking, yes he had something to offer, but you have to weigh that against everyone else who is wasting resources, there are far less Steven Hawkings then there are people with Alzheimers alone, no system can be perfect and losing him in return for gaining all the resources the others are wasting is a beneficial trade.
The basis is the optimization of society as whole(the resources as mentioned, no disability ramps, wheelchair elevators, crosswalk beepers), I even acknowledge that recessive traits hide and eugenics cant remove those traits, they just shouldnt be catered to.
Adapt or die, the world shouldnt have to match the lowest common denominator(which keeps getting lower as medicine improves).