It wouldn't work because you're simplifying this using deaths as the only measurement.
Hospitals are filled with people of every age in need of ICU being severely ill, just because older people have worse odds of surviving doesn't mean younger people won't get effected, so the outcome would still be a healthcare that's completely overrun, meaning non-existent healthcare for everyone due to overload. That's just the reality with multiplicative spreads.
Second point herd immunity will always happen at one point in the future no matter the strategy, that's the only way to get totally rid of viruses like this. It's just a matter of how fast or slow you make that happen.
UK tried your way in the beginning, but changed after pressure from leading professors and scientists. Sweden are taking your approach but the economy is still basically shut down because people choose to distance themselves since most people have parents they want to protect, just like yourself i imagine. The elderly and most fragile are totally isolated and they say they wont be allowed to come out until the end of the year. The virus still reached them through their asymptomatic caregivers so that proved to be a failure but unavoidable.
2nd waves almost always occur because viruses mutate and restrictions are removed. It's not exact science, there's an element of trial, error and adaption to it.
I would love to see an approach that would actually work without having to shut down the economy for a period of time, but it's just not realistic.
The real question is the amount of measures necessary and how fast or slow you ease them back to normal.
