[sgp_]

> Also, with enough time, all the Bitcoins would be dirty.

This is a misconception. Coins are only associated with the last identified node. So for example if I sent tainted BTC to Coinbase, sure Coinbase would investigate my account obviously. But the coins can be used from then on as "clean" Coinbase coins, until they hit the next identified node by blockchain analysis companies.

[wmf]

If Coinbase accepts the deposit. If they refuse it then the hot potato is back in your hands.

[sgp_]

Ironically, not necessarily.

If you sent funds to Coinbase's provided address and they wanted to refuse/refund it for some reason, your new owned output would likely be marked as clean and from Coinbase.

This may vary across circumstances of course. And they may decide to refuse to issue a refund.