We can roughly estimate how long that will take if we stay at R=1. That's maybe 100k new infections monthly in germany. Meaning it takes ~40 years to reach 60%. (83000k*0.6/100k/12)
Maybe it's less if you can get more aggressive with more immunity, but even if I'm wrong by a factor of 10 it's still years and the vaccine is the more realistic bet.
One way to shorten the time is to constantly increase hospital capacity, so that in each month lets you infect more people. Especially if plasma donations turn out to work to reduce severe cases.
Another way is to separate young people from old people more effectively. Then you might be able to permit 1m young people to be infected each month with the same hospital budget we have today
That's assuming that the only two outcomes of a SARS-2 infection are "dead" and "completely recovered". There are case reports of young and otherwise healthy adults who survived SARS-2, but where a CT shows the lung tissue mostly obliterated. Sure, they survive, but running a marathon or going on that diving vacation might be a sudden death sentence for them.
I hope we can get actual studies soon because the anecdata is scary to me. I hope these stories only make news because they are rare not just because it happens to be a celebrity:
We can roughly estimate precisely nothing until we know how many people have been infected, how many are immune and how long immunity lasts. We currently know none of those things.
I took the best case scenario: all tested become immune for ever. If you want add a 3x factor for unreported cases and you're still at 10 years waiting time.
Estimates make sense, especially if they proof your point even if you are off by a factor of 10.
Maybe it's less if you can get more aggressive with more immunity, but even if I'm wrong by a factor of 10 it's still years and the vaccine is the more realistic bet.