Why remove the skin and seeds of a tomato?
Texture is the main reason, but if you're going to be blending the sauce, there can be off-flavors from cracking open the seeds.  Even if you don't blend it, they can be these slippery little things that I never much liked growing up.

To reduce the amount of waste, you can :


cook the sauce, then put it through a food mill to strip out the seeds and skins, thus keeping you from wasting the gel around the seeds.
freeze the peeled skins, to save for when you're next going to be making vegetable stock.
collect the seeds and gel, then put it into a muslin bag and hang to let drip to extract 'tomato water'.  (you typically use crushed tomatoes for this ... I don't know for sure if the gel will go through the muslin).  Tomato water is strange as it gives good tomato flavor, without the red color.