I see the impact of railroads more on Loyalty and Empire Management than speed of movement.
As mentioned before, effectively they extend City Radius to wherever the railroad runs within your territory, and also edtend land trade routes infinitely the same way. That changes how you manage your cities for Everything and how you manage your Trade.
IRL railroads required huge amounts of capital, labor and production to build them and whole new types of industrial organization to run them, and they also required that the entire country be organized into time zones and regulated in ways never required before. That means they vastly increase the reach and intrusiveness of the government. That means the type and way the government runs also changes, and its relationship to the population, as well as the amounts of Gold and Production that government can access.
So, in addition to speeding up transport of military/civilian units, Railroads also change politics, gold, production, and loyalty. And the new distances people can travel easily (from 10s of kilometers a day to 100s) change the type and placement of Entertainment and Cultural benefits available, and the size of cities, and the placement of Wonders and National Parks - in fact, a case can be made that National Parks are impossible without the mobility of the railroad to make them accessible to the population.
Model even a fraction of all that, and Civ might start to get Railroads right for a change.