Specifically, if you're really concerned about a delta, removing the origin is good for visualization; it lets you just see the difference between two trends (in particle physics, you can show an energy excess this way). Likewise, for exponential phenomena, log plots are the correct choice, since uncertainty will be magnified for larger values. In both cases, of course, you need to include error bars, but that is always true. But I don't think you can "instantly distrust" someone who is using these techniques when they are valid.