I've looked into why coroners are elected as I have always found that very strange.
It's complicated. They are not elected officials in every county nationwide. Most coroners are former law enforcement, and usually don't have this as their only job. As you can imagine it's also common for them to be former or current healthcare workers. There are also deputy coroners that serve under the main coroner. I just checked, and my county coroner is former law enforcement, fire fighter, and EMS.
The most basic reason: coroners spend taxpayer money, so the taxpayer gets a say in who the coroner is. I get that, but I also think there should be requirements for running, even if the coroner is not the same as a medical examiner. But I'm not saying that you have to have a 4 year degree, 10 certifications, and have an IQ of 150 in order to declare someone dead legally.
Apparently some counties do have this requirement for the official; I don't know if this happens pre-campaign or post.