(1) The "Canadian government" doesn't do health insurance, the individual
provinces each have their own system.

(2) In general, provincial health insurance doesn't pay for drugs, OTC or
prescription, except for drugs dispensed to hospital in-patients, and to
some extent for seniors.

(3) It does indeed require a doctor's time and effort to write a prescription,
so it would save the system money to make the drug OTC, since the province
pays for the doctor visit but not the drug in either case.

(4) Each country decides which drugs should be prescription and which OTC.
One factor in the decision is whether the drug might cover early symptoms
of a serious disease, so people who buy it OTC might avoid seeing a doctor
until their disease has become difficult or impossible to treat.  Another
is whether potentially serious results may occur from side effects, or
from contraindications which the consumer might ignore.  There are many
others, and it can take a long time to decide to make a prescription drug
OTC.  You can't expect every country in the world to make the same decision
simultaneously.  Note that non-sedating anti-histamines such as Claritin
were OTC in Canada for years before they became OTC in the US.

So your evil-government-screws-the-taxpayer-to-save-the-taxpayer-money
argument above doesn't make much sense.