I'm curious if privacy can be done in a way such that it protects the identities of the transactions (both in terms of btc address and personal identity)
Can it be done? Sure. Look at Monero for example. Will it be done on bitcoin? I suspect not. Most people in the community these days actively welcome government regulations and control if it means a short term boost to the price. The same people are happy to trade their KYC documents for an airdrop of some worthless shitcoin.
If the addresses and other identifiable sources and destinations of transactions are already pseudonymous, the only way you're going to be able to identify who is doing all this is with documents.
Although KYC obviously identifies you immediately, there are plenty of other ways to lose your privacy and be identified. IP addresses and browser fingerprinting can link your real identity to bitcoin activities, blockchain explorer look ups, transactions, etc. There are operating systems and browsers which track all your activity and report back to their manufacturers. Giving out a physical delivery address when paying by bitcoin. Not using encrypted communication channels when sharing a deposit address or discussing a trade with someone else.