We have different plasma cutters at work, but the only one I'm familiar with is what we call the "suitcase plasma". I've seen our guys do some serious stainless cutting with that 110v model. Without further exposure to the world of plasma cutters, it seemed to me you'd need to be doing salvage work on an old battleship to need one that required a 3 phase hookup.
I assume there would be some advantage to keeping your load balanced on the electrical service, but not knowing what it takes to run the plasma cutter kinda makes it hard to quantify. The current could be so low that mixed in with your other loads it's inconsequential.
There's also a general misunderstanding over just how much can be gained financially by using 240v vs. 120v or 3 phase vs. single phase to run equipment. There usually is an efficiency gain, but you buy power, not amps. It takes power to run machines. Power is what you pay for, although some utilities penalize you if your power factor is poor. This is the result of inductive loads. Anyhoo, you'll get the same bill for running a 10A load on 120v single phase as you would for a 5A load at 240v single phase.........................chim