>energy required to vaporize one ton of iron produces .... so you would need a nuclear reactor.

it is less than 2500KWh - under $250 of nuclear generated power on Earth. The best - fastest and efficient - way to travel outside planet's LEO that is available today is solar or nuclear powering ion thruster, with only nuclear really beyond Mars. So anyway you come into the asteroid belt with a reactor. A submarine or icebreaker like reactor - 70MW - would power vaporizing of almost 30 tons/hour of iron. Note, that nuclear reactor in space is tremendously cheaper than on Earth as all the regulation, safety, etc. costs either disappear completely or reduced a lot.

You have forgotten many zeros.

If you produce a few grams of a precious metal, that cannot justify the trip until there.

To produce something of the order of one ton, which still seems too low to cover the expenses, you need to process something of the order of one million tons of iron.

With your estimation that could take several years.

In reality the energy consumption would be much greater, because one must cut chunks of iron and transport them to the vaporization installation, then also transport elsewhere the condensed iron.

So you would need a decent number of submarine like reactors in order to achieve an acceptable productivity.

There is no doubt that it would be feasible, but the problem is that at the current prices there would be no way to recover the expenses.