It seems illogical to me to make a soldering iron tip out of steel coated copper. If tin is a superior material (notice the anachronistic use of the term "tinning" used today), then why not just make the tips out of tin? Is cost the only reason? Seems crazy to me to put up with difficult soldering just to save a few dollars on the tip.
A soldering iron tip is a device that transfers heat from the heater of the soldering iron to the items being soldered. As such it's important that it be high thermal conductivity and high heat capacity. High thermal conductivity materials include diamond, carbon nanotubes, aluminum, silver, gold and copper. High volumetric heat capacity materials include iron, copper, tungsten and gold.
I've avoided mentioning items that won't stand up to soldering temperatures such as water and superfluid liquid helium.
Copper has a high melting point, and is just about ideal for a tip (and was used as such for many years) but it dissolves into the solder so the tip gets eaten away fairly rapidly. So a method of iron plating the copper tip (over a thin nickel barrier, IIRC) and then tinning (wetting) it with solder was developed and that is now standard. Unless the user physically damages the plating, the tips are very long life- and they stay tinned unless abused by sticking the tip into plastic or whatever.
Other materials are generally not as good in one way or another or are relatively expensive. For example, silver has similar thermal conductivity but 1/3 less heat capacity compared to copper.
Solid tin obviously melts at almost the same temperature as Sn99.3 lead-free solder and would alloy with lead-based solders, so it would be a bad choice, as would lead.
Edit: As @WhatRoughBeast correctly points out, tinning (wetting) of the tip with the solder being used is another requirement of the surface of the tip material. The liquid interface transfers heat much better than simple contact. That is one reason why we can't just use diamond tips- they would not wet (at least I assume not, and I'm not going to try it). Plain copper tips were sanded or filed to restore the shape, and to expose unoxidized copper, and then tinned before use. That's what you would do even today if you had to use a soldering gun or an old-style high-power soldering iron.
Tin melts at about 232°C. In the answers to this question on soldering iron temperatures, the lowest temperature given for reasonable soldering is 260°C, while other answers give numbers in the 300-370°C range.
Solder itself is made mostly out of tin, so clearly tin is not very rugged under soldering conditions.
The word "tinning" refers to coating the tip of the iron with tin-based solder.