To put those density numbers in a bit more perspective: the entire country of the Netherlands has a population density of 521 persons per km². This is including the rural areas. While I wouldn't want to be without a car and happily own two, I can take public transit within walking distance from home, and I'm on the far outskirts of the country.
The transit systems in both cities operate across the entire metro area not just the "city" proper.
Vancouver Metro Area: 2,463,431 / 2,878km² = 856 persons per km²
San Francisco Metro Area: 4,729,484 / 9,128km² = 518 persons per km²
(Numbers from Wikipedia)
>Toronto’s population could triple and the city would still barely have the density of Brooklyn (14,541)
Brooklyn is not a city. It's a densely populated subsection of one.
>crucially, Toronto’s population density is less than many other American cities including Philadelphia (4,512), Chicago (4,594)
I'm not sure why you think Chicago and Philly are not comparable to Toronto despite being being only 1% and 3% more dense. They're effectively all the same density for the purpose of this discussion.