Padding on bike seat or in shorts?

I use minimal padding in both shorts and bike saddle.  People think they need more padding than they really do.  I just use the thin chamois with my shorts and tri suit.

Desoto makes a padded cover that works really well from my understanding.

Nope...padding is not required at all.  I do my cycling in a Speedo Jammer swimsuit. It works well for swimming , cycling, and runner.  I have done hundreds of miles on the bike with it and never wished I had padding.  

In the colder month I cycle with my Asics running tights.  I likewise have put tons of bike mile in wearing them.  They likewise don't have padding.  There is no way I would ever swim in the running tights, but they work well for cycling and running in cold weather.  :-)

If you don't train with padding you adapt to be comfortable on the bike with out it.   If you train with padding you don't make that adaptation which leaves you with fewer options on race day. 

This is all true, and lots of people have a poor match between bike, fit, saddle, shorts, and butt.

It is my opinion that too often people stick with the stock saddle "just because" and combine that with overly padded shorts.  It's a good idea to try different saddles to get the right shape for your particular body.  Same for shorts.  And the riding position makes a huge difference.

I started road cycling in 2002 and triathlons in 2003, adding a tri bike in 2007.  After much trial and error and (time in the saddle), I've found what works for me.I ride a Selle Italia saddle on my road bike and fairly heavily padded Pearl Izumi shorts and I'm comfortable.  On the tri bike, I ride a Fizik Arione Tri saddle (much firmer than the road saddle) along with thinly padded tri shorts, and I'm comfortable.  Tri shorts on the road bike are not padded enough for the seating position and saddle, and the road shorts on the tri saddle will chafe like crazy in the aero position on that saddle.

As for the question about why pad the butt and not the shorts - I think it has to do with where the padding goes.  The shorts padding wraps around your anatomy, while the padding in the saddle is fixed.     Padding is a really personal thing and it may be that you could devise something for your seat that would work. The majority of padded bike seats on the market are far too wide and for a different type of more upright rider, so if you wanted to pursue this I would work on a custom option.