"This will be an ongoing issue as long as we consider "placing the data online" as an afterthought or an additional process."
Providing public API access into a production database (especially an old one) is going to be problematic for a number of reasons, and frankly that's always going to be secondary to whatever the actual operational reason-for-existence of a government information system. (though I think we'll start to see it "out of the box" from more and more vendors as demand grows) I agree, "open by default" is an attitude that can be adopted by an agency, but may not be so simple to implement on their existing information systems.
(Disclaimer: I work for Socrata) What a data publishing platform like Socrata does is accept arbitrary data of any size and shape, put it in a catalog with associated metadata, displaces it from the production system, wraps it in an standardized API, allows for multiple export formats, and allows for user-created charts, maps and filters, etc... It handles the public accessibility piece that the systems of record don't/can't/shouldn't.
Of course, the goal should be to get the data syncing as close to real-time as humanly and machine-ly possible for our highest-value information systems.