I might have the wrong idea but I think that tagging code as public domain makes it appears loose, abused, ephemeral, and neglected.
There's already a huge list of licenses that are easy to incorporate with company works and that still gives credits to the authors or at least mention the name of the people that wrote the program. Choosing to "leave" your code in the open, without real owner, without a person to contact in case something happen, without an email to reach for bug report wouldn't be a smart move.
I'm not sure about the sqlite team workflow but for other projects the use of the "Unlicense" doesn't seem right.
It's not as if using a license will restrain other person from using or contributing to the project.
There's a huge display of thousands of licenses you just need to choose the one that fit in your specific case.