If we're talking here only about web APIs where there is an economy (meaning that money changes hands), then I don't think that it's fair to say that most are doing it wrong. This is relatively new territory and it is taking time to flesh out the business models. Look, newspapers are still trying to figure out the business models.
Information consumed by eyeballs has different business models. You can paywall or you can have it ad-supported (or both). API clients don't have eyeballs, so ad-supported isn't an option. Microsoft has the Azure Data Marketplace, which is the only monetized API market that I'm aware of. My company provides APIs for cloud ETL that companies pay an annual subscription to use. You could say that Amazon Lambda is a metered API. My own opinion is that there will be lots of different business models. This is just getting started.
Information consumed by eyeballs has different business models. You can paywall or you can have it ad-supported (or both). API clients don't have eyeballs, so ad-supported isn't an option. Microsoft has the Azure Data Marketplace, which is the only monetized API market that I'm aware of. My company provides APIs for cloud ETL that companies pay an annual subscription to use. You could say that Amazon Lambda is a metered API. My own opinion is that there will be lots of different business models. This is just getting started.