And also the fear of an app (and consequently the API) getting hammered by the mobile equivalent of a clickbot (should such a thing exist), or some developer on the product accidentally programming in an infinite loop.
Oops, there goes thousands of dollars.
FWIW when I was recently involved in pricing an API, after much thought I decided the best option was tiered pricing with different rate limits (requests per hour) at each tier. At least with that structure you don't have to worry about angry customers with huge bills or customers bankrupting you with usage gone wild that they'll never be able to pay for.
The other risk of pure usage based pricing is that it attracts a cost-minimization approach to usage. That was my original plan but speaking to prospects put me off when I realized that many were willing to forgo all business sense and invest crazy amounts of development time to minimize API costs. And you still have to support them. (NB Yes you can have a base charge but many seem to think that inherently unfair when they have to pay for usage on top.)