The CE mark is worthless, since it is a self-certificaton.

The UL mark is valuable, as are the other test lab marks. However, while an ethical storefront would require it, Amazon does not. I've bought plenty of things that are not listed, and if I want safe products I generally have to include "UL" or "ETL" in my search. Even that doesn't always work, I've seen products on there claiming a listing in the title but photo shopping the place where the UL logo ought to be off of their product images.