Why have cells evolved to have both DNA and RNA? Would it not have been easier to skip the whole RNA step, and go straight from DNA (storage of genetic information) to protein (workers of the cell)? I don't claim to have all the answers, but some aspects are listed below.
1. The RNA world hypothesis proposes that RNA existed before DNA did. RNA can catalyze (help along) some reactions in the cell, a process usually credited to proteins. It looks like at some RNA might have been all that was necessary. Storage of genetic information, and workhorse.
2. Proteins would then have evolved later. With 20 possible amino acids to choose from to form proteins (as opposed to 4 nucleotides in RNA), proteins were more flexible, and could evolve to do the job faster and more accurately. They also evolved to do jobs that RNA was incapable of doing. The allowed for much more possible variation, a big advantage if selection for fitter organisms is necessary.
3. DNA is suggested to have evolved as genetic storage because it is more stable than RNA. The extra oxygen atom on the sugar-phosphate backbone of RNA, makes it more reactive, and therefore less stable than DNA. For storage, DNA is more reliable. Any researcher who has worked with both DNA and RNA can attest to the fact that RNA will degrade much faster than DNA does.