However, the stiffer a tire is the less it will deform thus less heat is generated thus less rolling resistance.
Consider why a underinflated tire has a higher rolling resistance than a properly inflated tire. The reason is the sidewall is less stiff and the contact patch is larger for the underinvested tire, resulting in more flexing of the sidewall and tread resulting in more generated heat thus higher rolling resistance.
When a tire hits an impact, a tire must deform to a certain extent. When sidewalls are flexible, the tire deforms easily over the irregularity with the vehicle losing little momentum. With stiffer tires, they flex less but the impact now has to be absorbed with wasted heat. In addition, road irregularities cause micro (sometimes gross) air or the tire leaving the road. Every small loss of contact creates higher rolling resistance, again as wasted heat from increased friction.
Sure, and overinflated tires reduce rolling resistance on smooth roads by reducing contact patch area. Hypermilers will use narrow overinflated tires and ride the ridge or painted lines to take advantage of increased smoothness where their choice of tires and inflation have a clear advantage. Smooth roads (with the ultimate being your beloved steel rails) are where this strategy wins. On other surfaces, it loses in every regard, rolling resistance plus handling, comfort, braking, and tire life.
The ultimate example of this are off road tires. Road tires will be skipping and hopping at their normal pressures. A coast down test down a rocky bumpy hill will quickly reveal that those large low pressure tires actually have lower rolling resistance under those conditions. Road tires are designed for the middle between those two extremes of off road and steel roads and have design criteria considerably different.
Bicycle tires are a different animal and it is difficult to directly compare them. Yet I have a constructive example. Wider road bicycle tires (to a point) are routinely known and tested to have lower rolling resistance (has to do with lower pressure and how the contact patch interfaces with road surfaces). Tradition and air resistance stop road racers from using wider tires with pave racing or cyclocross being exceptions. I often go out on group road rides with local clubs where I'm the only one with one and a half inch tires - the rest on around one inch high pressure tires. Not really any noticeable difference in coasting down hills with the group (we would just be talking a few seconds over 10 miles, less at higher speeds due to the aero advantage of skinny tires). But where the effects were dramatic where we had to do a quarter mile on gravel surface. Everyone but me immediately dropped speed and had to work hard to maintain that pace. I just floated along, not as in a smooth road, but far easier than my fellow riders.
If we had car tires with skin walls, they would have lower rolling resistance but higher rates of failure from the tire sidewall touching obstacles minus a protective rubber coating. Bicycle riders have that choice, and tires without that stiff rubber side coating roll better, but of course fail more from sidewall damage.
Besides the issue of sidewall suppleness and rolling resistance, tire compounds also contribute greatly to rolling resistance in a comparable way. They are the point of contact with the road, and the better they conform to the road surface, the lower the rolling resistance as they don't skip or deflect forward and back which creates wasted heat.
Bias ply tires are obsolete. They were lucky to last 15,000 miles. Any tire rotation was creating heat trying to tear the bias layers apart. Radial tires greatly reduced rolling resistance by guess what! Increasing suppleness, the ability of the tire to conform to the road surface with substantially less heat than standard tires. I was around for the Michelin radial introduction and bought a set of tires (much more costly than standard tires at the time) and they did last for the advertised 40,000 miles. Radials have improved over the last forty years, had a set last 85,000 miles on my last car. Rolling resistance improved as a result, otherwise there is no way tires could last so long if they created as much heat as previously.
Efficient green tires are designed for low rolling resistance. While tire design is incredibly complex, these tires are more supple by design. This costs them for some other attributes such as handling, but they are a good compromise for non boy racers and their effect is more noticeable mounted on more efficient cars. But feel free to go no compromise your way and start riding on bare rims.