While I care a lot about having a competitive marketplace, it's much more important to me that I and my family aren't poisoned. Are you saying that smaller companies can't compete with Amazon if everyone has to check that they're not poisoning us?
Yes, because this adds cost to manufacturing. Imagine if you yourself wanted to make and sell children's jewelry. How difficult would it be for you to get a lab to test all of the stuff you make? Could you make any money after you subtract the cost of these kinds of lab tests?
A large company has economies of scale. Finding a lab is a much smaller portion of the cost for them compared to you.
But I'm sure I must have missed why this general principle couldn't be used for other things that we don't want to be toxic.
Saying that the onus should be on stores is crazy, unless you accept that a company should have exclusive rights to your product at which point it become a licensed product and would probably be branded as such.
The catch is when they buy materials (like paint) that are cheaper because they don't comply. Either because they are made for a market with different regulations, or they have been contaminated some how.
Manufacturers may need to get certifications from suppliers about the materials meeting the regulations, but these won't be the cheapest option.