What you mention under 1 is fine, i use bitmixer.io and its good but 2 i don't really get. If someone is looking for bitcoin i think it's possible to trace them to your address on 2. If you have government looking for you/your bitcoin they can just ask Bustabit (your example) for their database and they will give you up easily
Bro, can you kindly please delete over quoting of my post?
As for your questions, in my opinion, both ways have advantages and disadvantages. And using "second way" is quite possible.
Briefly, at first , to "just ask Bustabit (my example) for their database " you need to know that address belongs to them.
In the second, bustabit (in example) do not have to rush with answers, i think.
In the third, bitmixer (your example) may answer to some/all governments too, who knows.
Everyone thinks and chooses what suits him.
I'm just trying to bring together variants.
It's easy to find out who is the owener of the address. There is a difference. Bustabit will keep their records forever and bitmixer (since we are talking about that two) claims they delete their records after 24 hours. They are long into game and provide TOR mirror to the website so I think they are trusted (not promoting them, just taking them as an example).
Anyway thanks for creating the topic, it's interesting one, looking forward for other people opinions and experiences