lol, I like to think medicine is a little more advanced in the 31st century
Not to jump on you, but I think the other thing you have to consider is that while the weapons have gotten more advanced basic human physiology hasn't changed much.
What I mean by this is a lot of amputations happened in the Civil War because they were using cannon and musket ball that was so big it would destroy bone, once that happened amputation was the only option. Infection was the other problem, but even in modern war that is just as likely to happen and a lot of weapons (especially of the improvised variety) are designed to almost guarantee that dirt, glass, and shrapnel get into the body. Body armor can prevent some of this, but not always. Antibiotics can't help much against this either.
A lot of 21st century weapons are designed to wound and maim (it's more cost effective and demoralizing to the adversary) and I'm not certain that it would be any different in the 31st century (I don't know if the Ares Convention has a "ethical weapons" section. I know nuke, chem, and bio are explicitly forbidden, but land mines seem acceptable).
The U.S. Army (with the exception of the Green Beret medics) put less emphasis on a field medic that can "patch you up, and put you back in the fight" and more emphasis on our MEDEVAC system.
The reason the US Army has enjoyed significantly lower causality rates in Afghanistan and Iraq is because of the "golden hour" principal of MEDEVAC. Body armor helped reduce the amount of shrapnel and foreign debris that got into the body, but opening airways, stopping bleeding and then moving the casualty back to a CASH within one hour (or as best as we could) resulted in the illusion that, "if they have a pulse when dustoff get's there, they're going to live" (No guarantee to not being maimed or cripple, but alive). Last I checked survival rates were around 90% but it was all dependent on the MEDEVAC and CASH, which again comes back to logistics.
Field medics and even common soldiers have a pretty good first aid kit, but arguably the most valuable item was clotting bandage and tourniquets, all so we could stop bleeding and keep them alive till they got to the CASH.
So I would submit that even with an advanced medical kit a field Medic is still fighting breathing, bleeding, and infection problems. If bone is destroyed or a serious infection sets in, the options are limited. If there is some type of nano-technology that clean up wounds to get out foreign debris out, that might be a game changer, but otherwise most causalities will at the very least probably need to get to a some type of surgery before infection sets in. This assumes they don't have other internal organ damage, in which case they need surgery likely within hours.
Also field sanitation and field hygiene is of the up most importance to most medics and military doctors because if you don't have a clean place to work you're going to infect your patient, and so many diseases occur when people are in close proximity in unsanitary conditions (there is a reason they call it legionaries disease). This is another reason why infection was so high in the Civil War era, and even during WW1 and WW2. Most medics and docs were always telling us to change our underwear, and keep our areas clean. (Remember that scene in Forest Gump where LT Dan talks to Buba and Forest about changing their socks? That is pretty accurate). Hygiene can be a mix of a logistics, discipline, and leadership problem, and it can be just as dangerous as any other bio weapon.
You can have some advanced tech, but humans probably haven't changed much.
