We don't actually know Elaine's conditions: even if we assume she was telling the truth, we know there is more to it than just cutting off ties with the MC.
Also, it's possible Elaine and the 'other' don't know the MC's conditions, either. They might not realize getting him away from Monica (et al) helps him inherit. They might just be focused on keeping the MC close to them in order to help with their own conditions or to get more info about his.
As for Lily, she wants the MC to herself but I doubt she'd want to be cut off from Katie for the next decade. So I'm not sure moving to the beach house is a high priority there.