Private sales are not anywhere near "impossible" in most places, but perhaps the BC government insurance and registration system makes it particularly difficult there.
I don't know if EVs are more commonly leased than sold outright, but it would make sense for buyers who are cautious about the risk of a unusual vehicle, and for the makers of cars that they might want to withdraw from the market. Leased vehicles can usually be bought out by the lessor at the end of the lease, but are more commonly turned back in to the leasing company, which could be the auto manufacturer... that would leave them with dealerships, or in auctions which supply dealerships.
EVs are relatively new in the mass market, and the newer a used car is, the less likely it is to be sold privately.
A quick check of AutoTrader.ca shows 513 Leafs at dealerships in Canada, 241 of them in B.C. (an even higher B.C. proportion than I expected). At the same time, they list 36 for sale privately in Canada, only 12 in B.C. This is just AutoTrader ads and I don't know how much that affects the dealer/private balance, but it appears that private listings are only a few percent of dealer listings, and B.C. is aligned with the rest of the country.
The totals for all Nissan models in Canada show higher fraction of private than the Leaf, but still mostly dealers; it may be that there's nothing special about the situation with EVs, but EVs are just still relatively uncommon.