Heavily subsidized?

It obviously varies wildly, but a road can cost $1,500k per lane km (NS highway planning figure). A multiuse path costs $10k per km (City of Toronto). That's 150:1 ratio.

And that's just construction, path maintenance is basically just snow clearance, roads are expensive; though maintenance data varies incredibly wildly based on how it's annualized and traffic volume.

Make every lane km of road built require the construction of 0.5km of path. Sure, construction costs increase 0.3%, but I'd wager the reduction in car use would see that recovered in maintenance costs (personal guess, not data driven).