IMO, the dev workflow is significantly worse, integration testing is harder and I don't see the value on "scale to zero", when the alternative is a $5/mo VPS.
If you are lucky enough to have your company go viral and receive a sudden spike in traffic, will the rest of the infrastructure tolerate it? Will your database accept hundreds of concurrent connections, or will it tip over?
If you need to engineer and test the auto-scaling capabilities of the rest of your infrastructure, is there value in not needing to think about the scaling of your APIs?
These may sound snarky, but they are real questions -- I used to administer ~300k CPU cores, so I have some trouble imagining the use-cases for serverless