1) HR (presumably taking direction from in house counsel) takes the position that it will be difficult to distinguish between a work sample test and an IQ test
2) We are a large organization with very broad roles. The Performance Team hiring for a Senior Software Engineer will probably want a different work sample than the Analytics Team...
Let's not dignify that argument. I absolutely believe you that your company has allowed HR to sabotage your hiring process, and that sucks. But let's not pretend HR is right to do it.
There's probably a solid argument for giving every candidate for the same role the same work sample test; otherwise you might naturally want to randomize some parameters or choose from a bank (if you think "cheating" is likely).
If you or anyone you know is interested I'm a software developer and spend a lot of my time on cloud architectures/containers/multi tenancy optimizations but just generally enjoy solving business problems with technology. In a past life I cofounded a startup that didn't turn out to be viable after going through an incubator (not YC). I have a resume, LinkedIn, Github etc.