In addition to what you've stated, examination of many genes provides evidence that a lot of genes evolved through a process of exon swapping. I read recently that the first organism may have started with somewhere around 1000 or possibly 2000 exons, and genes have evolved from mixing together exons and mutating them. If you examine many proteins you can see that they are made up of several different domains, and if you examine the gene each domain typically is contained in one exon.