Actually all rivited ring mail didn't come till the 14th century. People previously were using simply rivited-solid rings which where much less likely to fracture along the rivit. Roman mail was still heavier than Medeival mail and had less diameter rings meaning that a stab was more likely to get deflected.
And what the hell is modern mail?
And I think everyone here is forgetting Lorica Squamata and how it is way cheaper than mail.