The main reason is, of course, to prevent terrorist acts. The Financial Action Task Force (FATF) - the global money laundering and terrorist financing watchdog - states disrupting and preventing terrorism-related financial flows and transactions are an effective and 'essential part of the global fight against terror.'
The footprints left by terrorists' purchases, withdrawals and other financial transactions also provide valuable investigation information.
The Institute of Chartered Accountants of Scotland (ICAS) points out strict anti-money laundering rules make it difficult to hide illegal funds under layers of fictitious companies. They also strengthen checks on risky third-world countries and improve access to, and the exchange of, information.
However, as technology advances and terrorists become increasingly sophisticated in exploiting gaps or loopholes, the rules need to evolve with them, especially given the rise of crypto-currencies and global terrorist organisations.