The airplane/travel table is padded, but not for comfort as one might think.
When folded, the padding squishes creating a seal. That way if we need to quickly pack up, only one player puts chips in a tube and the table can be closed making a seal so that chips or cards will not fall out. Believe me, the hardest part of building that table was the padded rail (pulling vinyl and foam over a 1" rail with effectively 1/2" underneath to staple, and getting it around the corners... it was a Masterclass in fingertip gripping. It's the reason we never made more to sell. It would not be worth the cost.
As for the padded bed, Yes, my bed has a mattress. I suspect if I slept on my card table, I would want that padded as well. In fact, it I put my entire body weight on my card table for 6 hours, I would also want the rail padded. But I don't put the entirety of my body weight on my forearms or elbows when playing cards.
However, if you are ever in Nashville, you are invited to a game. I'll make sure you get time at the wooden rail table. If you actually find it uncomfortable, I'll publicly apologize. Until then, as a great man used to say, "you are talking out of your hat".