I can imagine SpaceX choosing to self-finance a mission to the moon and beat NASA at it.
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That probably does require some imagination. Starting with any incentive to do so.
“Starship will end up doing the whole Moon mission. Mark my words.”
To address your question, what is the incentive for going to Mars
To occupy it. Just look at Musk's t-shirt. Isn't the entire point of SpaceX to go to Mars? Everything else they do is just steps in achieving the occupation of Mars.