Wouldn't the very patterns of development be different (and more amenable to rail) if the state didn't spend oodles of money building nice roads to make sprawl livable?

At a high level, urbanisation rates increased through the road building binge of the 20th century.

Perhaps those new migrants to cities would’ve chosen to stay in the countryside without roads? Worsening the economics of rail.

Or maybe they’d use their collective voting power to get more rail friendly new towns built?

I don’t think the answer is obvious.

Before the road building binge there was the rail building binge, though limited to the largest cities.

As an example, see the history of the Metropolitan Line in London.

Sprawl happens when there is available undeveloped land. Roads are just a symptom.

People build outwards first and then upwards.

There is plenty of undeveloped land that people don't move to because there are no roads to get to.

We have more than a century of data showing that roads are subject to induced demand. If you build more roads, people move and sprawl (and take more trips in general) until traffic is once again unbearably bad.

If you build more lanes, more people move further out. Roads create sprawl.

And active urban planning avoids sprawl.

Also bridges and tunnels, which seem to be very expensive to maintain.

I disagree that it's difficult: excepting toll roads and "unassumed" roads‡, the subsidy is 100% (and most toll roads are likely subsidized at a substantial fraction of their cost, since the tolls are rarely high enough to be self-sufficient).

It doesn't matter whether the money used to pay for road maintenance comes from property taxes (like in Toronto), income taxes (Ontario areas not maintained by cities / regions / counties), or gas taxes (much of the U.S.?). If you're not paying per use of the road, there is a 100% subsidy on the maintenance of the road.

There are definite costs to not maintaining those roads (people won't move where there aren't roads; unmaintained roads will result in more costs to the people using those roads as their vehicles are damaged more frequently—which may result in costs to the municipality for not properly maintaining those roads), but we should not pretend roads are self-sustaining or aren't entirely subsidized.

‡ Unassumed roads are those built privately by the landowners in common and are not maintained by the local government. When used for private dwellings, these roads usually fall under the sway of the local government after a period of time, even if they were built initially by a subdivision subcontractor.