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It could but the Crew Dragon likely wouldn’t have the delta-v to land and return. That being said, I don’t think it’s crazy to do an “assemble in orbit” architecture consisting of multiple preparatory launches.
Hell, Starship is supposed to require like 10 refueling launches to go to the Moon. Couldn’t we just launch 10 Falcon 9s and assemble a badass landing system in orbit?
two launches, put lander in lunar orbit with one rocket, put the command module and crew up in another. Almost all of the hardware is man rated and ready to fly, just need a LM.