I don't buy any argument saying that an FAI must be able to modify its own code in order to take off. Computer programs that can't modify their own code can be Turing-complete; adding self-modification doesn't add anything to Turing-completeness.
That said, I do kind of buy this argument about how if an AI is allowed to write and execute arbitrary code, that's kind of like self-modification. I think there may be important differences.
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You might just be seeking status. You might feel like you gain status whenever you declare that you will be working on a new project, and you might feel that you won't gain as much status by finishing an existing project that people are aware of already. At least, this may be true until you gain a reputation for not finishing projects.