To be clear, they have closed high schools and universities, and kept open junior schools under the theory that many children would need childcare anyway (over 80% of families have two working parents). Enough parents are keeping their kids home anyway that they are sending out warnings. 50% of the workforce is now working from home, under government orders for employers to support it where possible. People who have higher than normal vulnerability can stay home even if they can't work from home and they will receive unemployment benefits. Employers can furlough employees for three months at half pay, and the government will cover the other 50%. 70% of Swedes say they have reduced social activities, cell phone data shows 90% reduction in Easter holiday congregation. I haven't seen it measured but it's plausible that the amount of in-person contact between Swedish people is lower than the UK or US.

If that's the case, then the question is not "did we really need to reduce activity that much" but "could other countries have achieved the same low social contact rates without enforcing it?"