Liquidity concerns aside, Bitcoin's pseudonymity does provide an extra layer of privacy. It's the electronic equivalent of cash. Which is more private -- bank accounts with real names and ID documents tied to them, or Bitcoin addresses?
The market is too illiquid to support really high volume money laundering at present, but that won't always be the case.
The $1,000/€1,000 thresholds are extremely low, 5x lower than the existing suspicious activity reporting thresholds that US banks are subject to. It's upsetting.
Fortunately, the Travel Rule hasn't actually been passed into law anywhere. For now, it's still nothing more than a guideline from the FATF.
This is quite correct afaik, as the FAFT "Travel Rule" is the crypto world's equivalent of US "Bank Secrecy Act" travel rule, which requires your bank to report identifying information in transactions to other money service providers and in financial instruments of $3,000 or greater, and depending on how your bank interprets the reg.s, they report at the $1,000 level. The crypto equivalent does not have the force of law behind it anywhere, but adherence to FAFT guidelines, scheduled to begin in June I believe, as a practical matter will be observed, or the non-observing country will be ostracized from trade agreements and conventions between countries. So money service businesses will treat it like a law.