We could reasonably expect any humans going to Mars to bring a lot of medical equipment, supplies, and trained personnel with them. If you need an emergency organ transplant, though, you're probably out of luck.
This isn't substantially different than the risks many people face on Earth, including tens of millions of people in the United States who lack medical insurance. Most people wouldn't accept those kinds of risks voluntarily, but if someone really wants to go to Mars they might decide the risks are acceptable.
If a Mars colony becomes well established with a substantial population, then the risks become less, as the colony would have the infrastructure and full-time expert staff one would expect to find in a typical hospital, and a larger population would mean more potential blood and organ donors.
My point was that you will have at least 1 room dedicated and filled with the best available medical equipment and smart people that have thought about what is most needed. There will be likely two doctors and multiple people trained as backups.
That is only on the first flight, over time, as infrastructure grows the medical facilities will grow as well.
Point being here it is not exactly a crazy proposition for somebody to go on that mission.
> A mobile hospital looks like USNS comfort - 70,000 tons displacement and over 1,000 staff.
You are looking forward way far. If there is need on Mars for that kind of hospital with 1000 staff, 700 Starships is not actually that crazy anymore. Not to mention there are likely lots of optimizations as they serve different functions.
Common, think about this for just a minute - how many medical staff and how many tons of equipment are required to staff even a small rural hospital? An MRI scanner alone weighs 20 tons. Where are you going to get fresh blood for transfusions, skin grafts, or a kidney transplant? Many medical supplies are perishable and won;t last the trip.
A mobile hospital looks like USNS comfort - 70,000 tons displacement and over 1,000 staff. If you could take it apart and sent it to mars, you would need 700 starships.
That's why, when US army deploys a forward operating base, or arctic explorers set up shop, they can't afford to bring an 'highly advanced medical facility'. They deal with basic injuries and stabilise the patient, and send him back to a proper medical facility asap. You can do that on the moon, but on Mars it takes 6 month to travel once every 2 years.
If you are one of the first people on mars, and your spaceship is not the size of a nuclear aircraft carrier, any kind of non-trivial medical problem is a death sentence.
"You would first need to prove that building such infrastructure on the moon itself isn't far to un-practical and more expensive then going directly from earth."
Look, you can argue that cities in space are too difficult, but if you want to argue that a Moon city is impractical but a Mars city is easy - then I think the burden of proof is on you.