Why do trains use steel wheels on tracks?

Answer: Steel-on-steel has low friction

Steel-on-steel has low friction ✓ — Correct! A hard steel wheel on a hard steel rail barely deforms, so very little energy is lost as it rolls: the rolling resistance is roughly a tenth of a rubber tyre's on a road. That is why one locomotive can haul thousands of tonnes. The price of hardness is grip: steel on steel holds only about a third as well as rubber on tarmac, so trains accelerate gently and need long distances to stop.

Rubber wheels would melt on tracks — Rubber would not melt; heavy trucks run on rubber all day. The problem is that a soft tyre flexes under load and wastes energy with every turn, and it would wear away fast under a loaded wagon. Steel stays rigid, wastes little energy and lasts for hundreds of thousands of kilometres.

Steel wheels cost less than rubber — Cost is a side benefit, not the reason. A steel wheel lasts far longer than a tyre, which does save money, but railways chose steel because rigid wheels on rigid rails roll with so little resistance that heavy freight becomes practical at all.