The biggest gaps between boys’ and girls’ performances, globally, are found in a) Nordic countries (very gender equal, huge efforts made not to distinguish between boys and girls at all if possible, and I think single-sex education is pretty much unheard of nowadays), and b) Middle Eastern countries (very sexist, constant casual differentiation between boys and girls, and mostly single-sex schools!)
Boys underperform compared to girls in basically all societies where girls have equal access to schooling (except in maths at the higher levels, where boys often catch up and then outperform girls at later ages). But in terms of where the gaps are big vs where they are small, the factors making the difference do not seem to be where people think they are.
One issue with mass-scale single sex schooling at the state level is that it would be harder to find good teachers without accepting pay scale differentials where male teachers are paid more. Women would be reluctant to work in all-boys’ state schools, and men might also demand more “danger money” (!) as it were, before being prepared to work in them. Yet paying male teachers more, or paying teachers of boys’ schools more, would be politically explosive and create accusations of sexism. In the Middle East, one of several factors why boys do so poorly compared with their sisters, is because they can’t get good reliable male teachers; the wages aren’t considered high enough for the difficulty of managing all-boys classes, and men are a lot less likely than women to be second-income earners who are in teaching because they are the caring, socially aware type.
Having single-sex schools at the macro level, with lots of state single sex schools, is easier to do in societies like Singapore where very harsh discipline for boys (including corporal punishment) is normal and widely accepted, as it makes boys easier to manage. Few people in the UK would be OK with this nowadays! Mumsnet is full of posters flipping out because they didn’t like the way their child looked in the photographs taken at the school residential etc; no way would they be OK with their boys being disciplined the way they are in places like Singapore.