There are countries that 'action' this exact policy. Take Australia for example. Unemployment payments are based on the concept of mutual obligation, where those receiving unemployment benefits must demonstrate that they are searching or training for future employment: https://www.servicesaustralia.gov.au/individuals/topics/mutu...
Those who are unable to work, based on certain medical eligibility criteria, do not have to meet mutual obligation requirements to receive the disability support pension: https://www.servicesaustralia.gov.au/individuals/services/ce...
> You can also contribute to society in ways that are not defined as work. What happens to someone that is taking care of children, or taking care of their sick parents? Should they be assisted financially, or not? If so, how do you define that?
Again, this is a policy question that is answered in Australia and which is implemented administratively via the 'carer payment': https://www.servicesaustralia.gov.au/individuals/services/ce...
I agree with your point that people will fall through the cracks and that there will be mistakes in administering any system like this. But that is simply the nature of a rules-based bureaucratic system, which trade off the ability to handle edge cases with scalability.