The target audience of FizzBuzz (i.e., those who fail it badly) are indistinguishable from you otherwise, and they outnumber you. They also do send in portfolios and past projects, simply they lie about who did the actual coding in those projects.

The exception is when a company is approaching you directly - then it would be insulting. However, if an outside recruiter approaches you, and then hands over to the company... again, you need FizzBuzz or such, because some recruiters are cheaters and will even help hopeless candidates fake their portfolios.

Wasting people time hurts - but accidentally hiring someone who'd fail FizzBuzz hurts orders of magnitude more.