system
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human
[Star Trek] What is the purpose of hospital ships?

Surely, with the amount of crew needed to maintain and run a normal starship, there can be no massive additions of staff and facilities on a medical ship, over your standard multi-role exploration ship, that could actually make much of a difference. I mean, by the 24th/25th centuries, cuts and burns are healed in seconds, bones can be mended in minutes,  organ transplants take only a couple of hours with maybe a day of recovery, even exotic plagues or infections seems to be cared for within 45 minutes. So why devote a large portion of the spaceframe of a starship to specific medical facilities, when cargo and shuttle bays make excellent triage space on a normal ship?  


Would it be to ferry medical staff to places where they're needed? Even at high warp, it would still normally take anywhere from an hour or two to a few weeks for a hospital ship to race across the galaxy, to a location, for assistance, and the assistance they could provide - I'm hard-pressed to see what that could be outside of what planet-side medical facilities could already provide. The same could be said of medical supplies.  


Maybe it's purpose is near-front line support, in the event of war or other calamity - like a 20th century naval hospital ship or a Mobile Army Surgical Hospital (MASH) unit of WWII or the Korean War. It still seems like a normal starship would be a better use, being able to ferry injured from a damaged ship, that is unable to move and has taken heavy losses, or a planet under attack, or what-have-you, providing triage care until they could get to a station, or planet-side base, already better equipped for medical purposes, and with more facilities, like engineering staff to repair damaged ships.
gpt
Generally, a hospital ship is used as a rapid reaction for massive catastrophes. Much in the same way that the U.S. will deploy a carrier group to a disaster zone to provide medical and logistics support, a Federation member planet that suffers some large scale incident that overwhelms their local emergency response capacity could get backup from a Starfleet hospital ship. 

For a lesser emergency, yes, you could just use a normal starship, either using it's own medical facilities or acting as transport for medicine and specialists being brought in or patients being evacuated; this is in line with Next Generation-era Starfleet doctrine that calls for versatile, multi-purpose ships able to respond to a broad range of incidents. But once an incident reaches a certain level (a plague that is affecting continents instead of just cities, or a meteor strike), you're better off using specialist equipment.