A finops person will need to understand the cost and the alternatives. This could add a lot of unnecessary friction to a necessary and reasonable activity.

This is why the engineer should be the one understanding the cost.

Yes. Everyone involved should. It is a non-functional requirement.

should they? The business needs to understand the cost trajectory of the service. But it's very easy for large organizations to be penny-wise and pound foolish.

A company employees engineers in the hopes of reaping value significantly higher than their pay in the future. Analysis takes time, time requires money - reviews require multiple people's time. If you are looking at 1k per month in expenses - but spend 1 month debating methods of saving ~500 bucks per mont at the cost of ~1 engineer. You can easily be looking at a 20+ month time to return on investment. Computers generally halve in cost every 2 years - so you're time to reach a 2x ROI can easily be 4-5 years. Most businesses need a return on capital of ~10% to justify investors not simply placing their funds in the stock market.

Bikeshedding is bad in all forms. Bikeshedding over cost is just one more thing to avoid. That is not an excuse to be completely ignorant of cost, though.