covid 19 – Airline flies, even though we aren’t allowed to enter Canada

The list of exemptions is in line with what other countries have been doing and is far from preventing anyone from entering the country. Citizens and their family, (future) permanent residents, temporary workers, etc. is not “almost nobody“. That probably contributes to explain why KLM is still flying to Canada (stats for Schiphol, with no distinction between carriers, suggest only about half of all flights to North America are currently operating). Freight can also play a role (if a plane is flying anyway and cannot be replaced or converted to an all-freight aircraft, they might as well offer tickets and save some money on refunds by avoiding to cancel a flight). For you, the end result is the same: until the flight is cancelled, the relevant EU regulation doesn’t apply.

Now, you’re right the airline won’t take you there if you don’t qualify for an exemtion but they are still ready to execute their end of the agreement, should you qualify for one. From their perspective, you are in a situation not unlike that of someone who couldn’t get a visa. Conditions of carriage typically include language to cover situations like these and specify that you (and not the airline) are responsible for securing permission to enter your destination. They might offer vouchers (see the comments and other answer) but have no reason to treat it as a cancellation (which would make a refund possible).

Since the airline won’t help you, another approach would be to turn to your travel insurance (if you have one) or to an industry compensation schemes but neither of these are likely to be good options in your case. Compensation schemes typically cover package holidays, not necessarily naked flights and have also been under pressure lately. Both might exclude pandemics from their coverage.