Your factor of under-representation of cases seems to cancel out the delayed onset of mortality at the moment.
The end of the flu season is incomparable with the demands on the health-care system due to COVID-19 since flu-demand is at least 1-2 orders of magnitude smaller. The advantage of the end of the flu season is that we can identify cases quicker.
W.r.t. lesions caused by COVID-19 comparable to the flu. Yes, both cause permanent damage. However, COVID-19 seems to attack more of the lungs and in general, both lungs, whereas influenza often is isolated to one lung. I am not a specialist, but I have read scary descriptions of COVID-19 lungs from specialists.
The stringent measures are already happening and the effects are already being felt. The stock market has responded by evaporating 4000 billion in value. Given the past lackadaisical response of government, it is likely we will see further effects either way: response or not.
If nothing is done and millions of people will get infected (think: 2 billion people) in a short amount of time (1 year), we will see widescale breakdown of services, global turmoil and panic. Hopefully, we will be able to slow the spread, develop a vaccine and 500 million people will get infected instead.