ETA: I just had reason to look at the Buckley AFB medical site. They run things the same way: call for an appointment, no sick call and no ER. If you need more urgent or serious care you're going off base.
The big deal is the use of the care line for any active duty service member to make an appointment that may be up to three days later for an issue that affects them now. OR, you can go to the emergency room.
So... they have an ER for urgent issues. How is that a problem? How is going to the ER, waiting around and seeing a Doc worse than going to an aid station, waiting around, and seeing an enlisted medic... and then being sent to the ER anyway?
This is about an Air Force base, not a det with a TMC. This place has a full hospital and even clinics on base.
...but does each unit have an aid station? Fort Carson has clinics, a full hospital 2 or 3 TMCs... and probably 20 unit aid stations, which is where sick call happens.
When people went to sick call on the AF base, where did they go?
To clinics and hospitals? How is that any different than going to the ER and waiting around in the first place? May as well get an appointment.
An armor battalion has an aid station. They have medics and a PA sitting around doing nothing important all day. They can screen patients, treat the minor cases and send the serious ones on. The medic to Soldier ratio is relatively high in maneuver units. TDA units run more like you're describing and I've described. They're lumped all together under a TMC run more like civilian urgent care facilities. Heck, at places like the Pentagon or other "office" assignments they don't even have sick call. You go to a local hospital or clinic. I worked places where I just called the directorate Sergeant Major and told him I was sick. No doctor visit, no sick slip... if I wanted to see a doc I had to go make an appointment at a civilian facility somewhere.
I don't know for certain but I suspect that having lots of medical personnel sitting around isn't the case in the AF. I suspect most "Squadrons" or whatever don't have many medics. Maintenance squadrons, admin squadrons, whatever. I'm guessing few or no medics assigned. So they don't hold their own sick calls, people go to the base clinics or hospitals, right? They either have to keep enough medics around to handle the flood every morning and have patients sitting around for hours... and have medical personnel sitting around with nothing worthwhile to do the rest of the day after the rush is over... or spread it out throughout the day with appointments. Fewer medics, fer people sitting in a waiting-room exchanging germs, smaller facilities... AND people who need to be seen NOW can go to the ER, still.
I mean, there's a reason the civilian world doesn't operate the way the military operates. It's incredibly inefficient... and military sick call isn't set up the way it traditionally is to provide fast, efficient care. It's set up that way to provide control and oversight by the chain of command of the troops attending sick call. It's horribly inefficient UNLESS you have lots of medics just sitting around. The Army does, some places, and when it does it goes ahead and uses it. I doubt the AF does very often. The military HAS to get more efficient. Costs are becoming important. Budgets and manpower is going to dwindle over the next few years.
The military sick call system is designed PRIMARILY to filter out malingerers. That's WHY units handle their own sick call before sending troops who need more care on to others... so they can catch the fakers. That's the WHOLE point of it. They don't trust Joe to be truthful when he says he's home in bed sick. They want a medic/PA/ Doctor to agree with him. The military is the ONLY place in the world where's it's illegal to call in sick when you're not. There's a reason for that. They don't trust you... for a reason, in fairness. Lots of people do try to get a day off from time to time.
NOW you're complaining because they've decided to believe you when you say you're sick. I mean, as long as your chain of command is reasonable and BELIEVES you when you say you're sick I'm not seeing the problem. If they make you go to work when you're coughing up a lung because you don't have a doc's order putting you in quarters that's kind of stupid and counter productive, but it doesn't sound like that's the case.
Short version: No sick call, but appointments for chronic issues and an ER for acute issues. Not seeing the problem.