In addition to being SQLite focused, I tell students to just use one open-source, cross-platform client: http://sqlitebrowser.org/
Sure, you could make the argument that I'm woefully preparing my students for jobs in which PG/MySQL/MSSQL is by far the standard...whether you're talking about web applications or dealing with legacy data files. But job viability is not in my scope...I argue that I'm teaching students the fundamentals of data and logical joins...that I use SQLite is merely an implementation detail.
That's how I feel about the CS 142 class...if students come out of that class being able to understand even an intermediate level of all those concepts...when they get out into the "real world", learning how to write for cross-browser compatibility will be well within what they can learn on the job. Just like it's trivial to learn the other variants of SQL once you've grokked SQL itself.