The fermenter chiller isn't really designed to cool boiling wort. Would it work? Possibly, but not efficiently. Just like you wouldn't use an open refrigerator door to air condition your house.
The objective in post-boil chilling is more than just cooling the wort to yeast pitching temperature. You want to rapidly get the temperature below the so-called food safety "danger zone" of 40F-140F (4C-60C). A rapid chill also promotes a good cold break, which means cleaner wort into your fermenter.
Since most beer yeasts ferment above the bottom range of the "danger zone", the target for your wort chilling should be something near your desired fermentation temperature and getting there fairly quickly.
Seven to 14 gallons of boiling wort has a lot of thermal mass that has to be dissipated before pitching yeast. That's a task for an immersion chiller or plate chiller. The role of a fermenter coil is to fine tune and maintain a specific narrow temperature range. It does this quite well, but it lacks the bulk chilling capacity to rapidly cool boiling wort.
Two different tools for two different tasks. You wouldn't use a pocket knife to cut a cord of firewood. Also the reason why atomic fly swatters never caught on.
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