When we were pregnant with my daughter, I asked my partner why she didn't just ust "daddy", but as you mention, triciaandann, it's not a perfect world!
We chose Papi and Mami because we both feel a little outside the norms. My partner is more butch than trans, but sometimes that differs with the day. I myself identify as a femme, but not in a het way, so I just balked at being "mommy". Even though they sound the same and mean the same to my kids, it made a difference to me.
I have been surprised by how many butch-femme couples we've known who have opted for mommy/mom, mama/mommy, etc. It's obviously harder to wrap my mind around than theirs!