Because (as @PaulOB explained) padding adds a fixed amount of padding within the border, and that remains the same no matter what happens to the text size. Height fixes the minimum height; if your content is less than that height, then there will be empty space at the bottom, but as your content increases, it will fill the space, and then stretch the table cell to fit.
This is one reason why I keep saying how important it is to know what content you intend to place in a container while building a layout; different approaches behave differently.