There are many factors that influence flex and rigid-flex PCB, here are some of them.
Tooling charges comes down to volume. For rigid-flex and/or flex prototypes and small volume runs, most are manufactured with laser cutting or some type of mechanical routing. This is used to create the surface mount features in the Coverlays, part outline, and if required, the outline of the stiffeners. Electrical testing on these lower volumes is typically done with a flying probe.
In volume production of flex and rigid-flex circuits, you need to switch over to steel rule dies or male/female punch and die sets. These steel rule dies are typically more expensive to create verses the laser cutting technique. The electrical test fixtures are also switched over to a hard wired test, which can be more labor intensive. Both of these factors can add an initial upfront expense, but it allows for a substantial reduction to the unit price of the part when you are dealing with higher volumes.
The primary reason for the more expensive PCB tooling charges associated for flex or rigid-flex circuit boards really comes down to the amount of manually created engineering programs a specific design may have. The other reason is the volume, but in production volumes we typically see that most customers recoup the additional expense in 2000 pieces or less.