The "piggyback" hx you mocked up will do fine on horizontal drain runs. It should live 100 years or more as a drain line. Just make sure the fresh water channel has a way to burp itself. Your heat transfer surface lies directly where air will accumulate if allowed to.
In an industrial hx, they use stainless because it is stronger and less expensive than copper. It is not an awesome heat conductor, so when the unit has to be compact, they use cupronickel (copper stainless) or (you guessed it) copper for the working transfer tubing. In modern industry, less expense translates to more return nearly always.
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