I agree that BK-BX cross-borough public transit is pretty terrible, but to reach even upper Manhattan, public transit should be used. I just mapped a route from a friend's place in Bushwick/Ridgewood to Columbia/Harlem, and it's 1hr both by subway and driving. And not that you would bike it with kids, but it's 16mi--pedaling is a 1.5hr trip on Google Maps, but class 2 ebikes can top out at 20mph.

I think the bigger issue would be why one has to drive an hr each way on a regular basis in a dense city, as it's an example of inefficient sprawl. A 1hr bike ride is essentially from AMS Schiphol airport to the old city center, covering everything in between--from accountants to hospitals to arenas and parks.