The rationale for this: door knobs are notoriously bad in terms of accessibility for disabled people. If someone cannot grip and twist, they cannot open doors. As such, codes like the Americans with Disabilities Act have (for years) mandated that knobs in public/institutional buildings be replaced by leversets.
Anyone installing access control may find themselves replacing doorknobs with levers as a result.
The exceptional aspect of Vancouver's mandate: the ban extends to private residences as well. Beyond public access, even homes are forbidden to use round door knobs.
Former gameshow host Chuck Woolery is outraged. Mr. Woolery is running for Congress (in the US, not Vancouver) and is pointing to the doorknob ban as another example of overreaching government, even to the point of building campaign promos opposing it:
Politics aside, I think the phasing out of round doorknobs is a net good. Better, more useful, and more accessible levers are available in the market, and cost is equal. Unless someone is just sentimental about knobs, there is no reason to use them.
However, do you think Vancouver has gone too far in banishing knobs in Canadian homes? Chuck does.