Pedestrians don't walk on streets. Pedestrians walk on sidewalks. Cul-de-sacs and crescents may inhibit movement of cars, but they don't necessarily inhibit the movement of pedestrians.
The City of Toronto proper is mostly post-war suburbia, it's mostly cul-de-sacs and crescents, not grid, but TTC still has twice the ridership of CTA. It's not about the layout of the streets, it's about the layout of the sidewalks and pedestrian walkways and trails. A cul-de-sac terminates or a crescent loops back before it reaches the arterial, but the sidewalk along that cul-de-sac or crescent can continue onward.
For example, look at this bus stop along Sheppard Avenue and the pedestrian walkway connecting to it in Scarborough:
https://www.google.com/maps/@43.7969...7i16384!8i8192
Another along Chinguacousy Road in Brampton:
https://www.google.com/maps/@43.7009...7i16384!8i8192
Cul-de-sac ending before McLaughlin Road in Mississauga, but the sidewalk doesn't end:
https://www.google.com/maps/@43.5982...7i16384!8i8192
Another walkway from cul-de-sac to bus stop near Martin Grove Road in Etobicoke:
https://www.google.com/maps/@43.7522...7i16384!8i8192
As the bus ridership in car-centric suburban Toronto shows, you don't need to have a street grid to have high transit ridership. You just need to have proper corridors for buses, and sidewalks and walkways connecting to those corridors. And fixing the sidewalk network is probably much easier than fixing the street network. Toronto is undeniably built primarily for the car. It is undeniably a car-centric city, but being car-centric doesn't have to mean ignoring transit. Just because a city is not transit-oriented doesn't mean it can't incorporate TOD measures.