Oh I actually know this one. Mostly historical accident and path dependence.

In medieval England, kings wanted to make sure that taxes and fines to the crown were properly paid, so they had their own officials in each county, who reported to the King rather than to any local officials. Sheriffs were responsible for tax collection, law enforcement (both arresting people before they could be tried and carrying out the rulings of the court). But they'd have to wait for the king's courts to actually come to town and hold trials and what not, so in the meantime the king's financial interests weren't necessarily aligned with the sheriff's.

So coroners were appointed to watch over county matters and represent the king's financial interests whenever the courts came to town.

When someone was convicted of a capital offense, their property escheated to the crown. That was an important source of revenue for the crown, so coroners would determine whether a dead body was the result of a crime or not, in order to make sure the crown wasn't missing out on some convict money.

Both the Sheriff and coroner positions survived the transition into American governance, but independence and democratic reforms meant that these previously crown-appointed positions needed to become elected positions. Most states kept Sheriffs and Coroners as county officials, and preserved some of their traditional roles and duties. Many coroners offices were renamed to "medical examiner" but basically still preserved the role of keeping stats on deaths. And without appointment by the crown, most states just chose to make these elected positions.