Essentially there are several takeaways. The first is what has been said before, but they make it really clear, the need is the get the infection rate r under 1. Then it is under control. Essentially they show that there are a lot of different ways to do that. Involving combinations of hygiene practices, social distancing, isolation and contact tracing, immunity... They do most of the simulations under an assumption that we will roughly triple our ICU capacity. (This is about what health economists think is realistic. But it won't happen overnight.)
The big points include that there is a complete false idea that "flattening the curve" means the same number of people get it over time. This was lost in translation when we started talking about flattening the curve but it is not the case. If you really flatten the curve fewer people will end up getting the disease overall. See the next point about overshoot.
Overshoot is why just trying to get "herd immunity" via infections as quickly as possible is problematic on several fronts. The main reason is that you over shoot the 60ish% of the population with immunity from infection that is needed for herd immunity. If you go the way of getting all the infections out of the way quickly you get 90%+/- of the population infected in a short time, so a lot more people die. If you get to herd immunity more slowly, you don't over shoot as much, and maybe 30-40% of the population never gets infected instead of only 10%. It is also problematic because of another big point...
... immunity, whether from surviving infections or from vaccines, is not likely to be permanent. Right now we don't even know for sure that you do get immunity if you survive it, but the working average is about a year, based on similar viruses. This could be off on either side, and will vary for individuals. But it is very likely that this will become seasonal. If we develop effective vaccines and/or treatments, then it will be something like the flu that is manageable. The interrelation of points two and three is that assuming immunity wears off (which is highly likely) if you go for getting to herd immunity quickly in terms of time, then you also compress the time when everyone is once again vulnerable. This leads to more spikes AND makes it harder to get back to r<1 via herd immunity because most of the population is vulnerable at the same time.