I am not familiar with this variant. However, in civil law countries you need an explicit waiver (like the CC-0 license), otherwise the duty to preserve attribution remains there even if the license said otherwise. That's because attribution is a moral right rather than part of copyright.

The argument against is that someone who then encounters the code without the notice will have no idea what license the code is under. They won't be aware of the BSD rights and disclaimers that otherwise should apply to them.

What we do here instead is explicitly say that you can include the Lil License text, or link to it instead — as we tend to do in these modern times.

That's just the thing. I want a license that is clear about my intentions when I provide them a copy. What ever copy they receive from someone else is not, and should not, be my problem in any way, I want nothing to do with that transaction.

Could somebody attach their own copyright notice and pretend to be the author of your work?

That is a good question indeed! My intent is absolutely yes. Do what you please just don't blame me for it. But I guess legally no. It's license, not a transfer, so I'm still the copyright holder, which creates some doubts, true.

The zlib license does the same thing and is OSI/FSF approved. http://zlib.net/zlib_license.html

I don't really see how it could do the same thing. It clearly has three restrictions in its text, none of which is present in 0BSD. Number 3 being the one differentiating the 0BSD license from most other licenses.

Also 0BSD is OSI approved, they call it free public license though