Being safe is a perfectly good strategy for an individual, but it's asking for trouble on a societal level.
Seems like good fodder for tabloid evening news and then just let it be.
It makes sense to me to make the safe option into the easiest, most obvious path to take. Stop labeling wire brushes as "barbecue brushes", and stop stocking them directly alongside the cooking tools. That's the form I imagine a ban would take.
The danger of hammers is obvious. You know to treat them safely, and so there's comparatively little trouble. The possibility of having an untreatable needle stuck in your throat unless you use your tools in the right order is rather less so.
I didn't say anything about banning unsafe objects, however. I think there's a case to be made for it if they're easily replaceable, but that's not the point I put forward.
Chainsaws, C compilers, C-4 ...
Certain industries would be crippled without these tools. Safety training helps.
Safety features tend to constrain or eliminate various uses, which may be needed in some cases.
Alternatively, safety features may be expensive (e.g., the mechanism that instantly stops a table saw when it touches flesh).
In some cases, great design can improve safety at low cost while retaining utility.
The question shouldn't be "is this safe", but rather "does a much safer alternative exist that works almost as good or even better"
That's literally every product ever.
I challenge you to come up with an example of something that's readily available to the general public that cannot reliably cause harm or death if used in a sufficiently ignorant way.
People intentionally eat Tide Pods. Should we ban all cleaning products that an average person is capable of injecting a lethal amount of?
Steel chainmail is awesome for cast iron, and probably safe for anything steel wool is safe for. For pans with coating (enamel or nonstick) where that's not safe, soap, water, and sponge works (sponges have the same shedding problem as steel wool, but usually higher contrast and harder to miss and fail to rinse out when they do shed.)
But focusing in on the rivets, there are two ways to look at it. The remaining fat that has undergone polymer-type conversion due to heat is seasoning, not dirt. Or if you really want to get in there, probably an ice pick.