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That's one legit use of a mixing or joining service.

Not saying there isn't tracability though those services (especially since we aren't ideal) since the point of the distributed ledger is tracability.

Something that was rather easy was depositing to an exchange, and just withdrawing; you lose the identity of the coins, at the cost of the exchange knowing the connection.

I think the traceability concerns are mostly handled since while it might be possible to infer an identity from an address that's sent to or from an exchange account, it's a lot more murky once those coins are moved elsewhere. If you know that address ABC belongs to me, and you see I sent coins to address DEF (which is entirely offline and using a brainwallet), and later DEF sends coins to GHI, you're left with the task of proving that DEF and GHI belong to me, and weren't me paying someone else.

What you're saying is correct, except you keep saying "wallet" where you mean "address". A wallet is a collection of addresses.

You can specify more than one input in a transaction, so that shouldn't be necessary.