Applications Today Without an API

I am doing a lot of research right now on quality web 2.0 applications for specific purposes. It really is frustrating when I find the perfect aplication with all the features we are looking for except for one. An API.

Why the hell do you go an build a really sweet application with killer features and you don't add an API.

It just seems like it goes against all logic these days to release a partial or no API at all.