Does your auto mechanic or plumber or doctor charge by the hour? No, they give you a price for what you need. And they base their price on both market value and their cost (including their time).
Fixed fee for a large project can go wrong badly because early mistakes or missed requirements can set the schedule back and increase the complexity of the work. Break big projects into smaller tasks that you can reliably estimate. Review progress with the customer frequently. Know the business value of your work, not just how long it will take.