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I am unable to find a portable inverter genset that can use natural gas of at least 12Kw. Is that because none exist?

None exist that I am aware of. Like the others have said, best to parallel two portable inverter generators together. For natural gas, you may need to install a conversion kit on each and you will likely get 10-20% less power output. I have the Honda EU7000is converted to run on natural gas and if I needed that much power, I'd either parallel a second one or go with a larger, water cooled standby unit like the Cummins RS25.

This guy has paralleled a few of the larger inverter generators, but none of them were converted for natural gas:

Maybe poke around his channel and see if there's any brand that has what you want and has a conversion kit available.