> Poisson is such an under-utilized distribution for these kinds of phenomena.

Yeah, Poisson distributions show up everywhere if you are paying attention. You can even use the theory as the basis for a fast, elegant algorithm to take parallel, weighted random samples. You can even do it in SQL!:

    SELECT *
    FROM Population
    WHERE weight > 0
    ORDER BY -LN(1.0 - RANDOM()) / weight
    LIMIT 100  -- Sample size.