The envy of the world
"It makes us wonder... how come the government-controlled Canadian health care system - which takes so much grief from those who defend our bloated, wasteful system - can provide plenty of vaccine for its residents and we can't?"
Assuming that the Canada actually "can provide plenty of vaccine", I do not have an answer to why Canada "can provide plenty of vaccine" for its residents. But I do have an answer why "we can't." Our country gets its flu vaccine from two suppliers and one of those suppliers was recently shut down because of quality-control problems. The exacerbated shortage of the current flu season was caused by this plant closure, but this is a problem for the current year. But why are there only two suppliers of flu vaccines in the US?
The reason is twofold: 1. prices are low and 2. regulations and regulatory enforcement - which increases the costs of production - have increased. Prices are low because various government agencies in the US use the market power they have on the demand side of the market to negotiate low prices for vaccines.
On the production side, although the production process has not changed much over time - especially over the past 4 years during which time shortages have become an annual right of passage into spring - increased regulatory pressures on the flu vaccine production process has inflated the costs of producing each unit.
When firms see that their production costs are increasing while at the same time finding the prices they receive on their product falling, well sports fans, that just ain't good for business. If this persists over time, firms take their resources to more lucrative markets.
Alex Tabarrok at Marginal Revolution has this post and this post on the subject. Russell Roberts at Cafe Hayek has this post on the subject. These posts give much more detailed analyses of the market for flu vaccines, including an anlysis into the production process in which they are created. I highly recommend them.