Sure, conversion would go up if it was in the first slot versus the last, but it takes effort (however little) to scroll through a carousel, so ensuring that we can measure the quality of the result and not just the quantity is really important.
This is one way I've tried to avoid the problem you describe. It's not enough that people can engage with the feature, but they need to engage with it meaningfully and in such a way that would encourage repeat behavior.
Another example of what you describe is that on our site if you search for "neon blue guitar", don't interact with the search results whatsoever, go back to the home page, click on a product on a carousel, and purchase _that_ product, it counts as a "successful search event," even though the search technically failed because they didn't interact with it in any meaningful way. To your point: PM is happy; user is not.
TL;DR it's really important to think through tests and how you measure success!
Depends, does that increase overall sales? Or is it ‘better’ to make the customer ‘walk past’ the other items to get to the thing they want (the way supermarkets make you walk up the back of the shop to get to the milk), and maybe buy something else too?