I don't think you need evidence. People who are concerned about cancer would be looking for the cancer warning and avoid those products, just like people concerned about the rainforest will seek out Rainforest Alliance-certified products. People who don't care, don't care, but for people who do, they make their decisions based on the information provided to them.

And I just think it would be cool if we dropped little hints to people about the best way to do common things, like cutting an avocado. Imagine if the world were filled with little tips and tricks everywhere we went. Tiny changes, but added up, might elevate life as a whole.

The Prop 65 warnings apply to basically everything, so it's difficult to avoid them. That doesn't mean that the warning is bad, just that the threshold is too low.

Giving radiation warnings at the level of a banana would be useless. Does that mean we shouldn't use Geiger counters?

You seem to ask the question in bad faith, as clearly this is not the right place to find out these statistics. Google is your friend. There is evidence that warnings, in general, do work.

There is also evidence that wired headphones, which don't have batteries in them, do not self-combust and therefore will not require such a label. A label that differentiates products is certainly useful.

There is also plenty of evidence that most people are unaware of the potential dangers of lithium batteries.

There is no parallel with Prop 65 warnings here.