Story: “It would be career limiting..."
This happens in a similar away at the small architecture company I work at. A client will pay for work, and then it will then become clear the work they have asked for is infeasible. However we are still contracted to do work. It benefits us to do this work and bill for it. I find it totally unethical to do any work after finding out that it will never result in a building, but my managers know that if we do the work we can bill for it. I think this story is the same, whereby the managers know the client will not benefit, but also that they will pay.
A recent HN post spoke about how employees are either aligned with a company (profit) or the overall goals espoused by the company. These goals appeal to the client. This story is an example of the OP being aligned to the client but not the company, and essentially how our economy is not aligned with ethical practice.