- Money that is "socked away" in savings accounts or investment portfolios reenters the economy through lending or through decreasing cost of capital for businesses.
- It is inherently better for Mankiw to write articles than it is for starving writers to do so. If anyone derived value from what the starving writer was writing, they would be getting paid for it and therefore not be starving (generalization -- there may be a few cases of highly valued writers being paid almost nothing and sharing their works for free to a wide audience, but I'm not aware of such). In the common case, that means that we are paying the starving writer for producing ~0 value, and decreasing the value that Mankiw produces, resulting in an overall decrease of wealth for society.
The fundamental misunderstanding you seem to be embracing is that the function of any individual in an economy is to pass the money they receive in wages forward to the next person in the chain. But this is not so: from an economic perspective, value is lost when less overall wealth is produced, so it's important not to encourage people in pursuits that hold no value to society as a greater whole. For example, society ought not pay artists that produce nothing other people want to look at for their services, nor should society pay programmers who produce software no one uses. On the other hand, society should avoid decreasing the output of those whose work is valued highly, like Mankiw's.
(If you derive some perverse value from having money wasted, then it would of course be fine for you to pay starving artists, but I'm arguing that society as a whole through the government should not.)