One way that the universal prior is superior to the one you propose is that it can notice that the machine alternates between producing heads-biased and tails-biased coins.

In this comment, I described another prior (still much easier to use that the universal prior) that could detect this pattern, and also noted another behavior the machine can have that my prior can't notice.

The advantage of the universal prior is that it assigns non-zero probability to all computable behaviors the machine might have, so that it can concentrate probability into that behavior if the machine exhibits it.