When we talk about AML, we forget that the inventors of the Blockchain and current developers want independence from conventional financial ties and are aiming to increase overall transaction efficiency by reducing costs and bureaucracy.
Anonymity was seen as essential to the user experience allowing anybody to transact with anybody worldwide.
It is obvious that this brings risks as the source of funds is always of interest to countries and tax authorities..
Tax is paid when ever there is a profit and it is doubtful this will change soon; while countries develop AML legislation for DEXs/DeFi, tax authorities will sooner or later also want this data.
DEX transactions will be possible be monitored initially at the gateways - thus a party will have to provide ID to trade but the value of the trade may well remain private.
There are tax havens worldwide as well as offshore countries where companies can hide details of their true owners.
DEXs and DeFI transactions are international by nature so these countries may be barred from permitting transactions or it could be that citizens in regulated countries will not be able to transact with unregulated countries.