The writers of the US constitution were well aware of how to enumerate positive rights, as they were common in the state constitutions, as well in many European countries' declarations of rights in restraint of monarchs. Many of them resisted this, especially James Madison, who called them mere parchment barriers and ineffective, even counterproductive. Madison's side mostly held sway, where the US constitution focused on the structure of government. The anti-federalists and other factions were the ones who pushed for enumerated positive rights, and they won only some concessions, like the Bill of Rights, which Madison and others worked to limit, such as phrasing some of them in negative terms.

You can disagree with Madison, but he certainly wasn't ignorant about these questions. He just felt positive rights were better secured through dynamic legislative processes within a stable and responsive democratic framework. The hard part is trying to maintain a responsive democracy. Without that positive rights are empty promises, anyhow, as they often are in these newer constitutions. One of the problems with making promises you can't keep is it delegitimizes government, which furthers the normalization of corruption and unlawfulness.