Why do you have to rinse rice?
It removes excess starch, so your sushi rice doesn't turn into nasty glutinous slop. The texture of the rice is very important, so you'll need to rinse it several times before you steam it. Make sure the water is nice and clear after the last time you rinse it, and make sure you buy japonica or similar: if you use regular rice, you may not get good results.

I wouldn't worry overmuch about the nutritional content of white sushi rice (you can starve on a diet of it). It's what you put into your sushi that'll give it nutritional value.