
Plus, even if it's harder to have back up in case of a fire hazard or more prone to error than more modern systems, it's not like evidence of your crimes being gone is a bad thing. For example, paper records are much more difficult to copy and smuggle out than computer files, and smartphones that are always online provide a clear opening for a security breach.
The use of outdated technology by the criminal underworld makes a lot of sense when you consider the security it provides. And while Marat was assassinated and Gianna technically committed suicide, the famous painting evokes the sense of suicide. Said political figure's death is the spark that lights the fuse that leads to a massive, insane political upheaval, befitting the implication that there's a war between the High Table and the Bowery King. Gianna's death seems built to mirror in some forms The Death of Marat, both the painting and the actual event: A powerful political figure is cornered by an assassin and dies. Besides the obvious connotation with the deadly underworld of the Wickverse, the second movie shows the parallel as more literal: Near the end, it is shown Charon personally drives Wick to the spot where he'll be executed, just like the mythical Charon would.
Charon is (presumably) named after the ferryman of Greek myth who carries those who pass away to the world of the dead.