This is a false equivalence.
When crossing the street, other people in cars don't want to actually kill you, and those crossing are generally aware and cognizant of the danger. The biggest mistake you can make is 'forgetting to look before crossing'; a lot of the time that won't kill you.
The setup here is very different.
The voltages involved in the wood burning process is far outside of most people's familiarity; your intuition for electricity just doesn't apply.
We're not just talking 'mains supply can be dangerous'; electricians routinely work on switches and such without bothering to shut off the circuit (even though this is typically ill-advised). Mistakes with mains, whilst they _can_ kill, usually just result in big bangs and breakers being tripped.
What you think 'protects' you just doesn't; your insulating gloves, shoes, wire covers, even air gaps; they could just fail you, and badly.
Even aware of this, knowing 'touching the probes kills me', a tiny mistake, such as 'brushing my insulated leg on the piece of wood I am working on, easily made despite being careful, has a very high chance of instantly killing you.
The only way I could see to make this process 'safe' is to not be in the same room as the equipment when it's connected to the power.