No, not really. You can’t “downgrade” the status of a Public Domain work. When a work is in Public Domain, it stays in Public Domain. You can, of course, create a derived work and license it with something else other than PD/CC0. And if someone does that (picks a work in public domain, creates a derivative work, licenses it with a more restrictive - even if open - license), while it is potentially restricting the free use of their resulting work more than they could, it is in no way restricting the use of the original work – it stays in the Public Domain.
If (and I am not sure about the scope of your question) you are meaning “new data starts being published as something else instead of Public Domain”, then yes, that would be - in my prespective - an huge step backwards. However, if the scope on where this is being thought of is considering an Open Licence, as defined in the Open Definition, as “good”, maybe there’s no preference there for some Open Licenses in detriment of others…