Why wouldn't they stay mixed as a liquid? They're highly miscible, if you leave liquid N2 out it can actually enrich with oxygen with time as oxygen dissolves i

Why wouldn't they stay mixed as a liquid? They're highly miscible, if you leave liquid N2 out it can actually enrich with oxygen with time as oxygen dissolves into it. You need to distill them to separate oxygen and nitrogen cryogenically. That happens in the boiling off part, but as another commenter mentioned you could pump out what you want to boil to avoid boiling the bulk liquid and causing the remaining liquid to be enriched in oxygen.