it should be illegal to trade in bitcoins that have ever passed through the relevant wallet
Whilst the bitcoin ledger is distributed, and therefore a matter of public record, 'bitcoins' as such don't exist as discrete entities, and are theoretically infinitely divisible (although technically the 'atomic' size is currently 0.00000001 BTC). It's not a case of bitcoins moving around, but of balances in wallets going up and down. All 'bitcoins' are perfectly fungible - if a wallet holds a balance, and part of it is paid out to another wallet, you cannot identify which part of it that is - i.e. what origin that part of the balance had previously.
What you suggest is impractical for two important reasons:
1) There is no global regulation, so someone in a country not respecting your rules can cash out their bitcoins.
2) If a wallet has a balance of, say, 1.45874354 BTC, and 0.0004323 BTC of that has come at some point from an "illegal" source, do you then say that any transaction in the future from that wallet is suspect, and, by extension, any transaction from a wallet that has had a transaction from it, etc.? What happens if someone transfers 0.00000001 BTC from a suspect wallet into a mining pool? Are you going to say that suddenly a large fraction of the network is suspect because those wallets receive payments from the pool's wallet?
Your suggestion is a bit like saying that all bank-notes that have ever been involved in the drugs trade should be removed from their current owners and burned. We can start by burning everything you have in your wallet. Let's include the bank cards as well for good measure.