As you mentioned, power-users bork their own data and power-users at big companies bork everyone's data at the company.

Another thing is that exposing an API makes you into a platform, on which third-party developers will try to build businesses. At this point you wind up having a small-scale version of Apple's dilemma. Third-party developers don't want you to encroach on their "turf" with first-party features, but it may be much better for your users if you're the one executing that feature. Third-party developers will try constantly to get you to do their jobs. You'll be locked into backwards compatibility in a way that you wouldn't be if you didn't have an API.

To be clear, this isn't an argument against exposing an API. Power users and their preferences are one thing, but another benefit is the ability to expand into foreign markets by partnering with local entities. If your software interacts with government regulation in some way, for example, it can require substantial interface changes and putting that maintenance burden on a third party more familiar with the government in question is a big win-win. This is especially true when you are in several markets, all with diverging UI needs - an API and local partnerships save you from trying to be everything to everyone.