Oh I totally agree that it's a great card in a lot of decks and will definitely see competitive play.
But I was specifically replying to the viability of a Barnes combo deck where there's no RNG at all (i.e. no other minions other than Barnes and the one you want to pull, let's say Y'Shaarj).
I don't believe your math, that 29% of the time by turn 4 you'll be able to pull off the combo, having drawn Barnes and not Y'Shaarj, so I'm going to do it myself.
First let's assume your starting hand after the mulligan has Barnes and not Y'Shaarj. From here, you just have to avoid drawing Y'Shaarj for four draws, and there are 27 cards remaining in your deck, so thats 26/27 * 25/26 * 24/25 * 23/24 = 23/27 = 0.85.
Now let's assume that your starting hand after the mulligan has neither Barnes nor Y'Shaarj. Then you need to draw Barnes and avoid Y'Shaarj in the first four draws. This comes out to 4(1/27 * 25/26 * 24/25 * 23/24) = 0.13.
And now we just need to weight those probabilities based on the likelihood of those being our starting cases after the mulligan, assuming that we hard mulligan for Barnes and always throw back Y'Shaarj. There are five pre-mulligan cases to consider: