I like sporty bathing suits, but many don't have chest padding, meaning that, when I hit the water, it's nipple city. Should I just let it all hang out?"
When I think of letting it all hang out, my mind goes immediately to an ungroomed bikini line, not the suggestion of nipple beneath a bathing suit. And to me, the "should" here is relative to your comfort level; if you are not self-conscious about this, keep on diving in the free world.
If, however, you are uncomfortable about any unwelcome glances, most swimwear specialty shops carry a range of suits with either built-in or removable padding.
My hunch is that athletic suits don't come with padding because they can affect performance. But as long as you don't care about shaving a millisecond off your freestyle, there are definitely designs that will fulfill your needs as far as form and function are concerned.