I'd also be careful with terms such as "insignificant" when we're talking about data. Suppose that tiny difference were significant. Depicting it as a bar would completely mask the difference, and truncating the axis would give the false impression of the bar's height representing the total magnitude. There'd be a similar effect with a line plot, but the line focuses on continuity and de-emphasizes height: it's not as big of a problem.

There are myriad ways to tell stories using data, and there are myriad ways to tell misleading stories using data. Each type of plot has distinctive properties that make it more or less appropriate to be used/manipulated in certain ways, so I'd hesitate to apply a static set of rules indiscriminately.