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The fan mounted to the hotend is definitely required, because it ensures that just the nozzle is hot, while the shaft is kept cool. If the shaft would also heat up, the filament in it would jam and clog the hotend.

The other fan is for cooling the print after leaving the nozzle. In some cases one can print without this fan (depending on material and situation). But in some cases it is an obvious advantage to enable print cooling (e.g. bridging).