Healthcare vs Other Necessities

Having a check-up every other year is an unnecessary and inefficient medical practice.
The Cochrane Library:
General health checks in adults for reducing morbidity and mortality from disease

Several reasons:

  1. Health care is far more expensive and unpredictable than the other things listed. Food, clothing, water, shelter, etc are constant needs and are mostly affordable. Health care costs may be very little for 20 years, then become six figures overnight. Budgeting for health care is extremely difficult.

  2. Many governments do say people are entitled to food, shelter, water and clothing. Even in America we have housing assistance and food stamps to help people meet these needs. Also in the US, there is massive public investment and regulation of sanitation and water to ensure everyone has access to clean water. So the things you list are things the government feels people are entitled to. People are also entitled to security, education, electricity, etc and collectively most people are perfectly fine with paying taxes and having government regulations to help achieve those things.

If you are asking specifically why the federal government should provide it, there is no particular reason except that the federal government is already doing it with medicare and veterans. By all accounts, the former is very successful, the latter maybe not so much. But if left to the states, then some will be very well served while others more poorly. Will Kansas provide decent health service when they cannot fund their public schools? But it is worth noting that in Canada it is the individual provinces that provide universal health care, subject to the minimum standards imposed by federal laws and regulations and this works well too. The big difference is fewer hands taking their cut. No insurance companies involved, no medical coders (who make lawyers look good), no for-profit hospitals, etc.