The gold standard should surely be what New Zealand's attempting: slam your borders, impose 14 day quarantine on new arrivals to stop imports, and throw every resource of the state into the most aggressive testing and contact tracing possible until the virus is starved of hosts and eliminated domestically. Not kept manageable, not mitigated, destroyed. It's what happened with the first SARS, and should, in principle, be repeatable with this coronavirus.
The direct benefits -- no more deaths from Covid-19 -- speak for themselves, but just think of the collateral benefits: the ruinous psychological consequences of fatalism and learned helplessness are replaced with a sense of victory; if it succeeded, domestic life could return to near-normal until a vaccine's available; and even if it fails, cases could be driven so low that restrictions can be substantially relaxed. Any "second wave" could be immediately attacked with the infrastructure established.
I can see no reason whatsoever to not at least try, with every resource we can muster.