Having the virus does not mean that you end up in the hospital or die from it. The idea of getting it small is to minimize the amount of virus that you are exposed to initially. A smaller amount of virus will take a longer time to build in your system to the point where you are having full blown effects, like the fevers, flu-like systems, lung congestion, etc. The longer it takes for the virus to build to those levels the better able your body is able to develop the antibodies and other immune defense response to the virus. If you get a large amount of the virus, for example an infected person sneezes in your face, then your immune system may not be able to effectively respond in time to the virus before you get really sick.
Go back to @snagged in outlet 3 example of exponential growth with the pennies in this thread or one of the others dealing with COVID discussions. Getting it small would be the equivalent of having 100 or 1000 pennies to start with instead of 10 or 100 million pennies.
The reason that there are people that are infected but are asymptomatic is probably due to them getting a small exposure to the virus and their immune system was able to fight the infection. The idea behind the insistence of wearing cloth or masks that are not N-95 rated is to minimize the amount of virus that they are exposed to initially. They are not really being used to prevent people from getting the virus.