Hourly billing puts the client and the consultant on opposite sides of the clock. Every hour saved is money the consultant didn't make. Every hour spent is money the client didn't want to pay. That's a strange incentive to build a working relationship on.
A fixed fee, scoped before anything begins, removes that tension entirely. If something takes less time than expected, that's not lost revenue, it's just a job done well. If something takes longer because of our own miscalculation, that's our cost to absorb, not an invoice we send.
The only thing that changes a fixed scope mid-engagement is something on the client's side that didn't arrive as agreed, and that's written into the plan up front, not raised as a surprise later.