The lockdowns appear to have also stopped transmission of most other infectious diseases. Notably, influenza.

Influenza has a lower R0 than SARS2, and it absolutely kills people. Worth destroying our economy over, all by itself? Ehhhh... I mean, we could have done this at any time, and we didn't, so no.

Nice side effect that translates directly to lives saved? Absolutely.

Does it offset other probable side effects, such as increased heart attack mortality from patients being unwilling to go to the hospital, or increased suicide risk from sudden business failures and unemployment?

No idea, like, none. Biostatisticians are going to be crunching 2020 for the rest of the decade.

The decision is not in reality between "destroying the economy" and "opening the economy up", because even in places that aren't doing strict lockdown, economies are cratering. Even if you opened everything up, people would still make their own decisions to participate or not in the economy, and right now, it looks like they're going to make the economically painful choice.

So then: if you're going to take on a massive economic hit just from altered consumer behavior, does it make sense to get the worst of both possible worlds by also relaxing regulatory constraints that are demonstrably saving lives?

You're drawing more out of that turn of phrase than I intended. Which makes sense under the circumstances, people are drawing lines in the sand and "open at all costs" is one of those lines.

It's not my stance. This is more narrowly-focused than that: we could end the flu season early, every year, by imposing lockdown from January 1st to February 15th.

But we don't, and this isn't the flu, it's a novel disease which kills many more people by even the most conservative estimate.

Still, as a side effect of the eminently rational (and economically painful) precautions which we've taken against it, ending the flu season a couple months early is a nice bonus.