Chemical methods would be much more efficient, but they would need huge amounts of chemicals that do not exist on asteroids, so they need to be brought from elsewhere.

It would be impossible to bring millions of tons of acid and of water, so if an acid would be used it would have to be regenerated, e.g. by the electrolysis of the iron-nickel-cobalt salts, which would also need a lot of energy.

Designing a process that could regenerate and purify the acid in a closed cycle, with no losses of any fluids, due to the difficulty of replacing them, would be a very difficult task. Nothing remotely similar has ever been achieved. On Earth, any such methods use at least vast amounts of water and air that are not recycled.

Also, any chemical methods would need to be performed inside a perfectly sealed installation.

Vaporizing iron and the other more volatile metals with an electron beam could be made in a partially open vessel, in the vacuum from the surface of the asteroid. The main difficulty would be to ensure that the metal vapor goes in a certain direction and not omnidirectionally, to avoid its condensation all over the installation.

When vaporizing metals in vacuum with an electron beam, you do not pass through a liquid phase, but the metal is vaporized directly from solid pellets. This method ensures a high efficiency of conversion between electrical energy and heat that is actually used for vaporizing the iron, instead of being lost in the environment.

Thus there would be no molten iron to be preheated, even supposing that there would be materials suitable for a heat exchanger working at such temperatures.

Moreover, even if one would first melt the iron in a closed vessel, heat exchangers transfer heat well only between dense fluids, i.e. liquids, supercritical fluids or at least gases at high pressures. The liquid iron qualifies, but not the iron vapor, from which transferring the heat would be bad. Better heat transfer could be achieved if the iron vapor would condense inside the heat exchanger, but for that a means to ensure a high enough pressure for the vapor would be needed, but that may be difficult to ensure without preventing its advance in the pipes. Liquid iron can be pumped with magnetohydrodynamic pumps, but for pumping iron vapor there is no easy method. Perhaps one could ionize the vapor, to be able to move it with electric fields.

A heat exchanger working at a temperature so high would tend to have a very high heat loss, due to radiation. It may be difficult to ensure that you recover more heat than the extra heat that is lost.

In any case both the attempt to use chemical methods or the attempt to make a heat exchanger for iron vapor would be engineering challenges that require solutions far beyond everything that has ever been done on Earth.

By contrast, vaporizing metals in vacuum with an electron beam is a routine technology on Earth. The only big challenge is that in normal vaporization installations the vapors go in all directions. On Earth this is not a problem, because everything around is covered with some thin metallic foil, on which the vapors condense. After that the metal foil is dumped if the evaporated metal is cheap, or it is sent to metal extraction by chemical methods if the metal is precious and it must be recycled.

On an asteroid, in order to avoid the deterioration of the installation, one needs either a method to move the useless vapor in a certain directon, e.g. by ionization and then moving with an electric field, or perhaps by making iron foil and covering the installation, and then working in batches, where one vaporizes an iron pellet, so-that the platinum-group metals remain in the pellet holder and the volatile metals are deposited on the iron foil, which is then dumped and the cycle repeats.

This is the only method that could be done with existing technologies, with minimal improvements over them.

However, it would not be worthwhile, as the cost of extracting thus platinum-group metals from an asteroid would be many times greater than on Earth.