Quarantine helps, perhaps in unexpected ways (and hurts in other ways)

The main purpose of quarantine is to prevent contact between people and, thus, reduce viral transmission. However, there may be benefits that go beyond the flattening of the peak. When you are sick and work long hours, the sickness is more likely to get worse. The main effect of the quarantine is that people stay home, drink tea and don't work. Under the state of quarantine, someone exhibiting cold symptoms is less likely to go to work. They are less likely to be stressed, less likely to ride a bicycle in the rain, less likely to run all day in the cold. If COVID-19 behaves like other coronaviruses that cause common colds in humans, the effects will be the same. People who stay home and drink tea are less likely to develop a bad cold -- less likely to have a cough, less likely to have pneumonia. 

The difference  between COVID-19 and the common cold is that the chances of developing pneumonia are vastly higher, but the general mechanism may be still the same. 

So, yes, quarantine is saving lives not only by preventing new infections and spreading the peak, but also by decreasing the odds that infected people will develop severe disease and need hospital treatment. 

OK, so any supporting evidence?

-- This effect may be seen in Wuhan:

"Patients who tested positive for the virus after January 23 had much weaker symptoms. This included a 50 per cent lower fever, 70 per cent lower feeling of fatigue and an 80 per cent drop in muscle pain."

The article attributes the effect to a mutation of the virus, albeit without providing evidence to that. I believe, that, maybe, it isn't the virus that mutated, but, perhaps, the change in human behaviour that is responsible. 

-- Medical professionals appear to have a higher chance of dying of COVID-19, compared to their patients. Also, dead doctors tend to be younger, have fewer pre-existing conditions and a longer life expectancy at the moment of death. Compared to the general public, doctors are more likely to be tested as well, so, mild cases will be detected early. This is partly because medical professionals are overworked and, in many cases, even continue to work in extenuating conditions well after they get sick. This is another reason to ask for help from countries who have already dealt with the pandemic ---- ideally, more equipment would be bought from China (and other places that have the capability to manufacture), and doctors imported who have dealt with the pandemic to build efficient teams that rely on a combination of existent personnel, imported personnel and young volunteers (who have already had the virus?) for dealing with it instead of asking insufficient personnel to work unlimited hours, which endangers both their lives and that of the patients they treat.

-- In South Korea, Singapore and Japan, where the pandemic does appear to have stopped, the weather is relatively warm. If this cold behaves like many others, warm weather should decrease the transmission rate, perhaps bringing it down so far that every coronavirus patient infects less than one more, thereby making the number of cases drop exponentially. 

We can also note that there wasn't any major outbreak (yet?) in a warm country where the normal cold doesn't usually take hold. The virus has been, without doubt, disseminated in the tropics, and transmission chains have been initiated, BUT, so far, we haven't seen any Italian style outbreak. In Italy, the outbreak is in the colder areas of the North, and not yet in the South.

I conjecture that warm weather helped Iranian outbreak as well, although I believe Iran to be underreporting deaths. The underreporting will become apparent in two ways 

-- the Iranian dead will be younger and healthier than expected. The main mechanism for underreporting is the lack of tests. Coronavirus deaths without positive tests are likely classified as having other reasons since many do suffer from pre-existent conditions.

-- looking at  the overall number of deaths in this period and compared to a similar period in other years.

Ways in which quarantine is hurting the response to the pandemic (beyond hurting the economy)

It's popular now to think of the pandemic as a war with an unknown foe because lots of people die, and also, war is dramatic and people and politicians like to think of themselves as heroes in a drama. However, this idea that everyone (and every place and country) is on their own is not there in war time, when countries work together and form alliances. The war and its aftermath are dealt with by volunteers and managed by people who help each other. Everyone on his own leads to mismanagement and results in hoarding of medical supplies just like people hoard the various flavours of toilet paper in places where they are not used, and in working medical personnel to death while everyone else stays home to play war games (or watches porn or parties on the sly). Wars rely on volunteers because there are not enough people in the system already to manage the wounded.  There must be a way for (young?) people (ideally, those who already have immunity to the virus? those without pre-existent conditions?) to train and help deal with the sick and with the delivering of goods and other aspects needed to manage this pandemic. This idea that it's enough to be home, hoard stuff, and let everyone else do everything becomes a problem once there is not enough "everyone else"... so far we see companies closing and limiting their services (e.g., even Amazon) and countries are sending their temporary workers home who were a big part of the "everyone else".