Hourly work turns every conversation into a meter. The client hesitates to ask questions. The builder hesitates to raise the thing that would take a day to fix but save a month later. Nobody says the useful sentence, because it costs money to say it.
A fixed price after a proper audit moves the risk to where it belongs, which is with the person who did the estimating. It also makes the scope honest: inside the agreed scope is included, and anything new gets its own quote before I touch it.
It does mean the audit has to be real. That is what Shape week is for. You cannot price work you have not read.