Interesting thought, but a couple caveats. A good economy self-regulates supply and demand for industries/job positions. This is especially true when all online job postings are online; it is easy for anyone to see what type of jobs are hiring the most. In an economy like ours, where unemployment is at a record high, if a section of the economy is experiencing a shortage, it is because those positions demand years of experience. Therefore it would take years for a government/institutional program to train workers for that field, which by that time the economic imbalance might have repaired itself. (Recessions typically don't last more than 2-3 years)

"This is especially true when all online job postings are online" -- as that true by definition, you probably mean "when all jobs are posted in public". That however appears not to be the case, by a long shot. From my vantage point it looks like employers at least in "tech" try to first use "networking", and only go to public channels when this doesn't yield. Often you have "stealth req" - "we have a candidate" - "create public req" - "oops we already found a match". Hence the name "LinkedIn" - it's meant quite literally.

Unfortunately that is very true and good point. I work for a newspaper company and was baffled during a conversation with the Classifieds-Jobs manager when she told me something to the tune of "95% of job openings are posted online, but 75% of the postings are fulfilled by internal networking, not by respondents to the job listing."