"I must have missed something. If there are government restrictions, why is there a shortage of fish in the first place? Didn't they work? "

Where have you been? Under a clam?
Yes there are government applied quotas, which most fishing communities have been grumbling about for years.
And no, they haven't worked because of a few factors......

The quotas should have been outright bans on certain species, but that wouldn't fly politcally.
The quotas were put in place too late and relaxed too soon before the population could rebound.
Improved technology means a greater efficiency in catching the buggers. You end up catching all of 'em rather than thinning the herd (so to speak). And if a few are undersized? Throw em back before inspectors get em (course they're dead, but nobody gets caught.....)
Some countries (Spain + Portugal in particular) tend to ignore such bans/quotas.

If the fish is cute and cuddly enough it may have a chance - see voluntary restaurant "bans" on swordfish.
(The Patagonian toothfish - aka Chilean Sea Bass is not being quite so fortunate right now, the "free" market for it is way too trendy)

The free market may work - just don't expect it to yeild any fish on your table in a decade or so......