How is this any better than the manufacturer just maintaining a database of legitimate parts (identified by QR codes) and then contacting the manufacturer when you want to know if a part is legitimate? About the only thing a blockchain would do is insulate you from the manufacturer's API going down. But even that can be solved by having the manufacturer simply send you a copy of the database periodically (and then contacting the manufacturer if your database copy doesn't have the part, in case it's newer than your database, although even that can be solved by having the manufacturer generate the codes in advance, so the database they give you can already contain the codes that will be used for parts manufactured over the next month).

Heck, you don't really even need a database for this at all, come to think of it. Just have the QR code contain a signed copy of the part identifier. You can validate that the signature matches the manufacturer's public key and that will be just as good as asking the manufacturer if it's valid.

Also, now that I think about this, this whole scheme (including using a blockchain) has the fatal flaw wherein a knockoff can just copy the QR code from a valid part. There's nothing stopping anyone from reusing the QR codes, and the knockoff will appear just as legitimate as the original.