Assuming a nationalized healthcare model, should the entire productivity of the nation be dedicated towards keeping a single person alive and healthy at the expense of every other conceivable economic activity such as building houses, growing food, manufacturing water treatment facilities, etc? Would it be macabre to deny them any amount of healthcare?

All economic systems allocate scarce resources which have alternative uses and thus rationing must always exists regardless of whether it is a free market, mercantilist, socialist, or as yet unknown economic system. Prices are a rationing mechanism within markets[1] but every other system will have its own set of one or more rationing mechanisms such as by-status, by-lot, by-need, by-survivability, etc. That necessarily means that there aren't enough resources to treat everyone for everything under all circumstances. Do you believe that all economic systems are thus macabre? If so I agree if only because life itself gives us hard choices, never utopic solutions.

[1] In terms of emergency healthcare by-need tends to be used even in market systems.