...which can really be done in any number base (and is even "easier" in base 2), so I'm still not convinced.
All we need to carry out the multiplication is the ability to multiply and divide by two! Somewhat simpler than the same operation in the Hindu-Arabic number system!
Maybe it is "simpler" but certainly not faster, because it glosses over the fact that division by 2 of Roman numerals is itself not exactly straightforward.
Roman numerals are a mix of positional and unary-ish "repeated symbol" --- that's what makes them hard to manipulate.
Both doubling and halving on a base ten counting board (e.g. of the style commonly used in Europe up until at least the 16th century; Roman counting boards were presumably recognizably similar, though not much physical evidence remains) are very fast and easy.
To halve any even group of pebbles, just remove half of them. To halve a lone pebble resting on a line (representing some power of ten), just move it downward into the adjacent space. To halve a number in a space (representing 5 times a power of ten), replace it by 2 pebbles on the line below, and one pebble in the space below that. These operations can be done very quickly and fluidly with a bit of practice. Maybe not quite as fast as operating a soroban, but not inordinately much slower either.
Historically nobody performed arithmetic calculations by writing down a bunch of intermediate steps on scratch paper using Roman numerals (for one thing, paper wasn’t available in the time of the Romans and both papyrus and parchment were expensive). Roman numerals are just a way of recording the finished answers to calculations done on an abacus (counting board).
From what I understand ancient Roman schoolchildren did most of their writing on wax tablets. It’s not clear when writing slates were first used; one of the earliest known examples is apparently 11th century India, though I’m not sure if they used chalk or some other writing material. See https://en.wikipedia.org/wiki/Slate_(writing)https://en.wikipedia.org/wiki/Blackboard
So to correct your statement: this was quite common in the 18th–20th century, well after the introduction of “arithmetic” and Hindu–Arabic numerals, which were popularized in Europe by Leonardo of Pisa’s 1202 book Liber Abaci (mostly material translated from Arabic sources).
Before that (and for a few hundred years after in most parts of Europe), most calculation was done with counting boards.
In other words, it's just the shift-and-add algorithm: https://en.wikipedia.org/wiki/Multiplication_algorithm#Shift...
...which can really be done in any number base (and is even "easier" in base 2), so I'm still not convinced.
All we need to carry out the multiplication is the ability to multiply and divide by two! Somewhat simpler than the same operation in the Hindu-Arabic number system!
Maybe it is "simpler" but certainly not faster, because it glosses over the fact that division by 2 of Roman numerals is itself not exactly straightforward.
Roman numerals are a mix of positional and unary-ish "repeated symbol" --- that's what makes them hard to manipulate.