why 13.56 MHz is an ISM band

Pretty simple question, why 13.56 MHz was on the first place declared as a ISM band? I know some other bands such as 2.4 GHz were designated as of unlicensed operation due to the abundance of commercial equipment using them (such as microwaves as 2.4 GHz is one of the absorption bands of the water molecule).

So what about 13.56 MHz?

Good question, but my guess would be "why not 13.56?" It had to be SOMEWHERE.

As far as my curiosity has led me, the inclusion of 13,56 MHz was propesed by the USA, the UK, Canada and Australia in the International Radio Conference in Atlantic city 1947. The reasons for allocating ISM bands were that:

"The apparatus for which frequencies are proposed, permits the achievement of many unique accomplishments . The industrial apparatus is used, among other things, for the rapid drying of glued joints and plywood, controlled surface haldening of metals and curing of rubber, .plastics and wood in important industries".

Ans apparently 13.56 MHz has traditionally been used for dielectric heating of wood, i.e. wood drying. So, someone in the wood drying industry back in the 1940s had powerful friends!

On track of conspiracy theories? Your conclusion is already disproved by the above quoted text, I think. In fact there are many applications all over industry and medicine. Technically, SW frequencies have been first available for generation of higher RF power with acceptable efficiency and effort. So it's quite obvious why 13.56 MHJz has been the first important candidate. I don't know however, what motivated the exact frequency choice.

The idea of ISM frequencies is to reduce pollution of other bands from ubiquitary RF sources for purposes that existed before.

You are missing the point. It is clear that there is a need to allocate certain frequencies to industry and medicine, but the interesting bit was that 13.56 MHz was favoured among many other possible choices just because there were some industry in certain countries using it

Yes, I know. What I mean is, that many people have been using SW frequencies for RF heating already in the 1940er years. The list you quoted potentially applies to 30 or 50 % of the industry. As far as I'm aware of, none of the applications is bound to an exact frequency. So for the time being, I assume that the choice of specifically 13.56 MHz is more or less arbitrary.

In a historical sense, it would be interesting if e.g. some manufacturers of RF equipment or industrial applicators actually favored 13.56 MHz and enforced their interests. But that can't be concluded from the quoted text.

For plasma staff as well, pretty good looks small loop ( impedance active part around ohm ) antenna tuner and some KW transmitter. Much better is here...
61.000 GHz 61.500 GHz 500 MHz 61.250 GHz Subject to local acceptance
122.000 GHz 123.000 GHz 1 GHz 122.500 GHz Subject to local acceptance
244.000 GHz 246.000 GHz 2 GHz 245.000 GHz Subject to local acceptance

why they stopped with 244.000 GHz . I`ve seen 600 GHz devises with dielectric waveguides.