I came here to say exactly this - the purposeful imprecision in plots doesn't come from squiggly lines (which I consider unprofessional in many contexts), it comes from the lack of axes numbers. That first xkcd plot is the worst possible combination of communicating false precision while looking silly.
Context is also important. Sometimes, your audience will want to know exact numbers and imprecise plots will look bad. Imprecise plots should only be used to explicitly show a trend, which your audience should be expecting. If this is the context, they'll understand and squiggly lines are unnecessary.
I disagree with this. It drove me nuts when my first-year economics professor had a perfect Excel graph containing two crossed straight lines to demonstrate supply and demand. None of it made sense to me until she showed me a graph from her third-year course with actual data in it. xkcd-style graphs would have helped me with my understanding, as would drawing them on the blackboard.
Context is also important. Sometimes, your audience will want to know exact numbers and imprecise plots will look bad. Imprecise plots should only be used to explicitly show a trend, which your audience should be expecting. If this is the context, they'll understand and squiggly lines are unnecessary.