So the reason you don’t “just show counts” is precisely because of fluctuations in the denominator (the population). Deaths per 100,000 standardizes by the population so let’s make a fake and sort of exaggerated example. I’d say one year there are 50,000 deaths among a population of 100,000 the deaths per 100k estimate is of course 50,000 deaths per 100,000. Now let’s imagine the population double somehow by the next year and this time 100,000 people died. The deaths per 100,000 estimate comes out to…50,000 deaths per 100,000. So this tells us that the rate of overdose deaths did not change between the two years despite the populations changing dramatically. This is why counts themselves are not an informative statistic unless it’s amongst a stable population. Counts would be more useful if it was say the number of ED visits for overdose for a hospital and that hospital was trying to measure the volume of patients they see in a given period of time. Even then they would likely be just as if not more interested in the percentage of all ed visits were for overdoses.

You seem to be confused about deaths due to other causes somehow impacting the denominator, I think? The population is of course whoever was alive in that year so I don’t see how more births or more deaths is relevant because for deaths they obviously won’t be included in the population for the following year and births don’t really change dramatically enough to have great enough of an impact on the denominator but either way babies can still die from an overdose, it’s tragically sad but it does happen, so they should be included in the denominator.

This is a perfectly appropriate graph and I made several very similar to this as part of my thesis research on the opioid crisis.