You are still simply arguing that the study in the OP is wrong.
Because it DID compare schools that were fully remote, to schools that were fully open. So any conjecture about the motivation of parents, or how many of them would actually choose to send their children to school, are already part of the reality of what happened.
- The longer schools engaged in remote learning the more students' learning was hindered.
- The sooner schools returned to in-person learning the less students' learning was hindered.
- Communities were schools engage in remote learning did not see the spread of COVID mitigated.
These are all facts. Everything you are posting is conjecture about what might or might not happen. The study is the result of what DID happen.