Couldn't they do a chip and pin style hardware solution where a security chip generates a response using a unique secret algorithm?

That would work — until someone decaps a few of these chips.

They're already doing something similar, after all.

But that's really not the case here. Making secure computing elements like TPMs or HSMs, or Apple's Secure Enclave or the plethora of other devices out there is a solved problem. You can decap it and try to get that data out of it but at the very least with the current state of the art you can make this very unlikely to succeed and extremely expensive to even attempt.

Handwaving away all of this as just a minor nuisance is silly. An attacker would have to find some unknown side channel or try to physically modify the TPM to get at the data, either approach means the attacker has significant resources, certainly well beyond the means of our hypothetical attacker. Heck, it's been speculated that even the NSA couldn't get data out of something like Apple's Secure Enclave without risking destroying it in an attempt.

Wouldn't you need to decap every individual chip you want to compromise?