I went down a different path of “if necessary”, but it underlies your question of ownership and value. Paying for the value as one would IP is an extension of the value transferred in a transaction. The less you know about the counterparty the more you will require in collateral or return for the credit risk.
The need to exchange personal information comes from incomplete transactions where credit is extended and debt comes into existence. All parties need to know each other sufficiently to extinguish the debt. Information needs to be sufficient to ensure the debt is settled with the correct person, and conversely, to find the person should the debt not be paid.
There’s no difference between P2P transactions than a loan from a bank. Yes, a bank takes as much information from you, but you know everything about the bank, too. Information is the nature of an incomplete transaction whether a loan or a deposit.
Does a bank need to know the source of your funds? Of course, not, but like having FDIC insurance in the USA, or simply a vault to hold cash, KYC is a requirement for doing business as a bank transacting in American dollars. But this is not about KYC, it is about personal information sharing requirements.
I know you probably thought my next line: bitcoin fixes this. Bitcoin’s instant transfer of value allows closure of transactions in real time. If for some reason, the transaction is purposely incomplete, such as prepaid rent or utility bills in an arrears, the need to exchange information can be reduced but not eliminated completely by using time locks with one of two multi signatures.
But again this is a function of incomplete transactions and the need to know how to recover one’s value in case of default still exists. One can avoid all of this by not using the dollar system, and not taking on debts/extending credit.