...that were more aimed toward determining the means and manner of death more than any criminal responsibility. The need for them as a civil process was much greater before modern technical means. Many people use the titles Coroner and Medical Examiner interchangeably, but we shouldn't.
Today's Medical Examiners are almost universally MDs and most often are trained, experienced Pathologists, and they have Pathologists working for them who perform autopsies.
Coroners in past eras were elected officials, and interestingly were not always required to have a medical background. In fact, Coroners functioned much more like civil court judges presiding over lawsuits than people who performed post mortem examinations.
Many Inquests were also Autopsies, where the Coroner would empanel the jury, open the proceeding with a stenographer, and then surgeons and/or MDs would perform a post mortem examination of the body right in front of the jury, render their expert opinions before the jury under oath, and the testimony and autopsy would be the evidentiary portion of the proceeding upon which their verdict would be informed.
There were plenty of reasons Coroners Inquests were regularly performed that had nothing to do with crimes. Many jurisdictions by law required the cause of death recorded on death certificates or record books to be an expert opinion or the finding of an inquest. You see similar reasons today for why autopsies are and are not performed. If a doctor signs off on the death record as having been present, in attendance or treating and the death results from a known or treated condition then that fills the expert opinion requirement for the death record, whereas a person who hadn't seen a doctor in years who was found dead unattended would be required to have an autopsy and the pathologist would fill out the death record based on the examination results.
Why did anybody care all that much beyond the obvious reasons like a concealed murder? There were plenty of reasons. In colonial and pre colonial times in England and her possessions, the property of those who committed suicide were forfeit to the Crown- Every farthing, even if that meant it left a family to starve to death. Obviously in such cases if there was any possibility of doubt, the family might benefit from the honest judgment of a Coroners Jury comprised of six solid citizens rather than that of a Crown official who usually pocketed a piece of the seized assets. Life Insurance was another reason- Most policies in past eras would not pay off for suicide and some wouldn't pay UNLESS the death record clearly showed that the death was NOT suicide. An inquest verdict was in such cases binding on the insurance companies, and if they still balked such findings were great ammo for lawsuits to compel payment. Civil War and other government pensions were another consideration.
Sometimes Coroners Inquests were convened to positively and legally identify remains, which would be a big deal if all there was left were bones, cloth scraps and hearsay. An Inquest verdict legally identifying remains might be the difference between a poor widow or orphaned children collecting a pension, bank accounts in probate, life insurance proceeds, or all of the above.