While the circuit is rated for 16A, it typically will be protected by a 20A breaker, which will generally not trip for the time it takes to use up the single rod.
That would be a 20A circuit, not a 16A circuit.
Here in South Africa a socket outlet is nominally rated at 16A maximum, but the cable in the wall is rated for 20A, and is protected by a 20A circuit breaker. Typically you have 2 socket outlets per breaker, in a single outlet box, though you can daisy chain a near unlimited number of sockets on one breaker providing you do not exceed length of cable for voltage drop. Typical use would be adjacent rooms having a single breaker feeding the socket outlets in the room, mounted back to back on the wall, and the kitchen might have 2 or more breakers for outlets depending on the size, but they normally are very frugal socket wise, typically one per room in the house.
In Australia/NZ I do understand they can either be 16A or 20A outlets, but even there the 16A outlet will still be able to handle a short period of welding using a 2.5mm welding rod, as there you are between 80-110A or so, so the input power draw will be lower than 30A.
Admittedly a welding plant is the only home use item that can draw much more current than a single standard ( for any country) socket can supply, but they have such a low duty cycle in home use ( 30s on, 10 minutes weld prep, slag removal, setup of weld) so are usable without needing to have a dedicated high current socket and cord set for the welder, which you do need with proper high duty cycle welding equipment that is rated for near continuous duty welding at max power.