Through common practice, these identities are treated as disposable and therefor generally ignored. But stating that the currency is explicitly designed to disallow accountability is not an accurate representation of reality.
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Edit to add a practical example for clarification because this is being downvoted.
If the FBI conducts an effective warranted search + seizure of a mob safehouse, seizes a large safe, opens it up, and finds either:
A) Gold bricks
or
B) Bitcoin wallet private keys
In case (A), they can maybe correlate records, reports, statements, and other evidence to possibly determine the rightful owner of the gold or goods laundered for gold.
In case (B), they can check the BTC ledger against fraud reports that contain bitcoin wallet public keys, then publish a public statement asking people to prove they own any matching public keys -- because bitcoin, by it's fundamental nature, is more accountable in a way that enables recourse and refunds.