They could just leave the servers running and let people continue to use with almost zero upkeep.
The sense I get from reader being discontinued is that it was being kept alive as a best effort, and the effort was becoming too complex, too difficult to take on without real staffing. I suspect "leaving the servers running" was what they were doing for the last few years, and it wasn't working anymore.
Technically, one or two engineers probably could keep something like Reader going, a drop in the bucket for Google, a rounding error. The true cost is not the upkeep, but the costs of the risks. If not investing any significant resources into upgrading and maintaining Reader means some snafu over personal data leakage, then you're looking at being hauled in front of Senate panels, and EU regulators, and civil suits.
Remember, Reader was written a long time ago by an understaffed and under resourced team.
Makes sense, until you realize that Google makes $10+ Billion in profit, and almost all of it it's because of the trust and goodwill factor from the online crowd. Once you start to maximize everything and refuse to leave a penny on the table, that trust goes