Good points Rabbit. Technically, they currently don't even know if getting, and recovering from, Covid-19 will protect you in the future. There are, obviously, many diseases that you can catch over and over again, the common cold, which is a different strain of Covid, is a prime example. They won't be able to know for sure until they are able to regularly test for Covid-19 antibodies as currently they are testing solely for the presence of Covid itself. The good news is that here in the States, the FDA just announced that they have approved emergency authorization of the first antibody test.
Short analysis: Antibodies are what your body produces when fighting a disease. There are a number of different antibodies that your body will produce when fighting any given disease. The important one that they will be looking for is a particular antibody that your body only ever produces once. This will then allow them to test a patient for antibodies and if they find not only Covid antibodies, but the one particular antibody, they know it is the patient's first infection. If they find Covid antibodies, but not the one particular antibody, then they know the patient has been reinfected. The working theory at the moment is that probably, this will work like a number of other diseases out there in that once you get it, you'll pretty much be good to go assuming you recover. Unfortunately though, they don't know that for sure.
But yes, the concept of herd immunity is very important here, and its a big reason why in general people are encouraged to get vaccines when they can. There are some children for instance, who for medical reasons, can't get a vaccine, but if everyone else gets the vaccine, then those children are at a much, much, lower risk of getting said disease since there's nobody to catch it from.
The other question will be that even if getting, and recovering from, Covid enables you to at worst, fight it much easier in the future, can you still transmit it? Maybe you become a carrier even if it doesn't really affect you. This is a very real and frightening possibility. Already they are estimating that between 25 and 50% of people infected with Covid may show few, if any, symptoms. Good for that person, not so much for the general populace since it is very communicable.
Just a quick update from the relatively small area I reside in. The wife's hospital had a patient who was in the hospital for non related reasons. While there, it was believed the patient had developed a urinary tact infection (UTI). Patient was treated for the infection but two days later still had a fever. Patient was finally tested for Covid and moved to an isolation room while they waited the several days for the test to come back. Up to that point though, the patient had "exposed" roughly 50 employees. Fast forward almost a week and the patient is confirmed positive. As are two employees. Several more employees have been home sick, but "are not sick enough to test". The problem of course is that all those employees obviously also "exposed" numerous other individuals. There are many hospitals that are not even testing their employees unless they absolutely have to because they don't want to know the results since they don't have the personnel to operate without the confirmed positive employees.
Bottom Line: Stay Home as much as you can folks!
Edit to add since seeing Zen's post: They actually are testing a vaccine in the U.S. right now. It has been injected into the first live patient (skipping animal testing). The problem is that they now have to wait 14 months before they can call it a success in order to make sure the cure isn't worse than the disease so to speak. From there it would likely be about another 4 months to mass produce the vaccine. You are right in that they have had success with some treatments and hopefully those successes prove repeatable and are not just the result of somebody being better suited to recover. The big difference too between the flu and Covid is the onset of symptoms. The flu tends to have symptoms start pretty quickly which then limits the amount of exposure. Covid you might not develop symptoms at all, or it might take up to two weeks.