Actually, there is. The UK strategy explicitly aims to avoid a peak come autumn/winter, you want it to go through enough of the population before summer ends. Too fast and it overwhelms the NHS right now, too slow and it will overwhelm the NHS in November.
I completely agree that it is a risky strategy, but unlike the general sentiment in this thread, I don't think it's an obviously bad strategy, and I absolutely think that everyone arguing against it are also engaging in a lot of wishful thinking regarding people's willingness to self-quarantine and obey government recommendations aimed at containing it.
Try harsh containment measures in the US, and 20% of the population is going to go "fuck you it's a Democratic hoax/Chinese conspiracy/Deep State population control scheme, nothing's gonna stop me!"
At least the UK strategy takes the unwillingness of the population into accord, locking down all retirement homes is much more doable than locking down everything.
The NHS is already overwhelmed. Right now. We are firmly in "too fast" territory. There is no amount containment, starting from now, that will be too much - the exponential growth is already getting away.
Also, why would that be less viable than locking down all of society the way for example Italy has done?
Again, the load on the health care system depends completely on the demographics of the people who get infected.
By isolating and quarantining people in risk groups, the load on the health care system will be much lower.
The gamble is this: By letting the virus spread indiscriminately through the part of the population that is not at risk, the load on the health care system will be manageable, the death rate will be nowhere near the current measured ones, and once the virus has passed, you have herd immunity in your population.
But if you argue for harsh lock down of everything now, you are also gambling. You are gambling that you can delay the spread until there is a vaccine, without knowing how far away a vaccine is. You are gambling that all the other countries get a handle on the virus, without knowing if they will.