Naive question, since I'm not familiar with the aircraft parts marketplace: Can the elements of the paper trail be hashed and published publicly, and can then those hashes be factored into the blockchain?
The irony is that what would actually make tangible improvements to aircraft part documentation would be more centralisation, since this allows a lot of cross validation of data on part ownership, maintenance intervals and hours/cycles data with other records regulators keep like data on flight paths and doesn't require sharing of commercially sensitive supply chain and operations information with people who don't need to know. And if you can't trust the regulator not to secretly falsify records, you've got bigger issues....
Yes, of course. But what makes the logical content of the documents/elements in the "paper trail" something that cannot be represented as text files or perhaps photographs?
In a word, trust. You can represent the information digitally, including via scanning, but you cannot digitally guarantee that the representation matches the paper copy; and the paper copy will likely hold in any disputes absent evidence of manipulation of the paper copy.