UHC is false advertising. What you are taking about is universal DISEASE coverage. Ill person has " right" to get care to treat DISEASE and , nopefullly, as a result become healthy again.
If you were concerned about HEALTH for as many people as posiible, because of the " universal " term in UHC , you would argue for population wide prevention. Clean water and satitation. Safe roads and vehicles, surveillance systems. Laboratories. Etc. etc.
There was a good program on NPR a couple of days ago on environmental health. The magnitude of impacts on health status dwarfs by several orders of magnitude what UHC does to finance doctors and drug companies.
More than a billion people do not have access to food. Would the World Bank recommend to give out food randomly as well?