After the death eaters take over the school after Dumbledore's death, I understand it became mandatory for all students to attend school but my question is why didn't students go to other wizarding schools, like Beauxbatons, Durmstrang, or Koldovstoretz?
The quote from the novel is that they're obliged to attend Hogwarts, and Hogwarts alone:
‘Ron, as we’re on the run with Harry Potter, the most wanted person in the country, I don’t think it matters. If I was going back to school, it would be different. What’s Voldemort planning for Hogwarts?’ she asked Lupin.
‘Attendance is now compulsory for every young witch and wizard,’ he replied. ‘That was announced yesterday. It’s a change, because it was never obligatory before. Of course, nearly every witch and wizard in Britain has been educated at Hogwarts, but their parents had the right to teach them at home or send them abroad if they preferred. This way, Voldemort will have the whole wizarding population under his eye from a young age. And it’s also another way of weeding out Muggle-borns, because students must be given Blood Status – meaning that they have proven to the Ministry that they are of wizard descent – before they are allowed to attend.’
The implication is that the decree specifically states that young British witches and wizards can no longer go overseas to be educated or be home-schooled. Obviously this quite closely parallels the German government's Reichsschulpflichtgesetz (federal compulsory attendance law), passed in 1938 as one of the actions of an ascendant Hitler administration.