Many recipes ask for peeled and seeded tomatoes, which I find both wasteful and too hard work.
What is the point of removing seeds and skin of tomatoes? Just texture and presentation? Or can it actually change the food's taste?
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.
It depends on the tomatoes. Sometimes the skin and seeds are SO bitter. I recently made a sauce and it was inedible because of the bitterness, so i made a new one with tomatoes from the same batch and removed the skin and seeds and it tasted delicious. Often winter tomatoes are the ones to watch out for. Summer ones tend to be much sweeter and can be used whole.
If you don't want the liquid or seeds, squeeze it out. What remains is the skin and pulp. If you don't want the skin this can easily be removed by blanching the whole tomato and removing the skin first.
Tomato and peppers are in the nightshade family. When I roast red peppers I do the same thing, remove the skin and seeds. I feel this intensifies the flavors and improves the textures.