A blowout will definitely make your hair more voluminous than a relaxer will. However, if you shampoo your hair, your hair will revert to its natural state.
If your hair is long enough, then your new growth will also be straight, but again, when you shampoo it goes back to its natural state.
Yes, there are people who just get their hair pressed every month so they do not use relaxers.
If your hair is thinning due to relaxer, then getting a blowout will give you thicker hair. It will be more maintenance, but if you want to have thicker hair, you will have to give up the relaxer.