Requires agility
In a development organization dealing with change, the ability to change direction is vital. Agility has become a more prominent competitive parameter than ever before.
Adjusting your "start position" may be necessary to meet customer and market demand. It is a need that can happen overnight when you need to act quickly to keep the flow in development. Time-based contracts both require and give that readiness and agility.
In bringing a consultant on board, the simple time-based contract terms make it possible to get resources quickly, so development and progress do not stop.
However, a fixed-price agreement involves much time to define a scope that can then be a starting point for a price. Furthermore, fixed-price contracts often reduce flexibility and the ability to handle change, as project scope changes require you to revisit the original agreement.