Who has said it is going to "magically" go away in a month?
Long term effects? What are the long term effects of any respiratory illness once you are cured? It is a novel coronavirus, not a whole new never before seen category of virus. There are coronaviruses that cause common colds.
As for the transmission of a mild case to somebody vulnerable, that is true of the flu as well although apparently worse with COVID-19. The solution is to test people with mild symptoms so that they know to stay away from elderly people if they test positive. The solution is not to disrupt the world economy.
South Korea is doing a ton of testing and data from there will capture many more of the mild or asymptomatic cases. The serious illness and mortality rate in South Korea will present a more accurate picture of the actual rates of this virus.
For active cases, South Korea currently has only 0.5% serious/critical cases. So far they've had fatalities in 0.68% of confirmed cases. The fatality rate will likely increase somewhat as the recently detected cases "age." Regardless, data from South Korea indicates that this virus is "worse" than the flu but it isn't 10 times worse like some predictions.
Even in the US, listen to Governor Cuomo talk about the cases in New York. Obviously, he is no friend of the current administration. Even he is pleading for calm and stated that only a handful of the nearly 100 cases in New York were hospitalized. If the media reported the flu like this every year, you'd think the world was ending also.