I like how deeply Baez thinks about the problem, but back when I was trying to figure it out, my reasoning was much simpler. Basically I just decided that keeping the binomial theorem true without exceptions was very important, so 0⁰ should be 1 by fiat. (If you set it to any other value x ≠ 1, then (0+1)¹ ≠ 0⁰⋅1¹ + 0¹⋅1⁰, because the left side is 1 and the right side is x.)