Except then they need to ensure that all the equipment on their line was produced by trusted suppliers with the same level of disclosure. Ditto all software which touches anything in the manufacturing process. It's turtles all the way down, see also "on trusting trust".
Just a few of the mountains which need climbing: First, you'd need a (actually) random sampling not just one (keep in mind any ASIC you test is likely a write-off due to tamper-resistance). You'd also need a high assurance supply chain to ensure your verification isn't premature (as well as sufficient levels of tamper resistance/evidence). You'd further need to verify the software around this hypothetical ASIC is free of bugs. You're restricting yourself to software which can be performant on older slower process nodes. You (almost certainly not an ASIC company) need to have an in-house ASIC shop, or you need to vet an external one (sounds cheap and easy for the average business). In fact, you need vetting of your internal staff at all stages of this process.
You are making this seem _much_ easier than it is. There's a reason this product, which there is definitely a market for, doesn't exist (and that reason is much more mundane than the cryptolluminati not wanting it to "get out"). Consider that Google did something like what you're suggesting. It took them years (and they're Google), what chance does the average person/SMB have?
In the end, it is the attempt to create a positive proof in a system that is not a defined formal system (real world vs pure mathematics). Impossible - as you say, you need to place your trust somewhere. Even if it's your own abilities. But that trust can always turn out to be not justified.
You suggested that they verify or perfect every person or thing in the entire supply chain. That was ridiculous. I suggested they or trusted, third parties simply verify an ASIC. That's doable. Matter of fact, people already tear down and image ASIC's on older nodes for fun. A number of companies and labs tear down modern ASIC's to reverse engineer them for understanding or finding patent violations. ChipWorks is top company in that space.
So, it's my recommendation of a practice that's being done right now vs you're recommendation to change everything in an impossible way. I stand by mine.
Just because something is technically possible doesn't mean the average company should do it. Security is about trade-offs.
If it's that, then it was a decent attempt at explaining how big the problem is if one wants to trust every step. Good news is you don't have to as I illustrated. Just a small number of third parties doing a tear down. They can even be enemies reviewing same thing with equipment made in opposing countries for best effect. Old trick of mine. :)
However, seems to me that if you are not Snowden, this is one of the smaller worries. Compared to all the other phishing, malware and so on.