The alliance is so far just in the Hogwarts board, not in the Wizengamot. Perhaps they feel it’s a limited alliance with a limited purpose, and can be broken off if the purpose at hand changes—safety of the students in Hogwarts.
Even so, I agree that we haven’t seen what exactly the people outside Lucius’s faction and the House of Greengrass got as an inducement to enter the alliance.
The alliance is so far just in the Hogwarts board, not in the Wizengamot. Perhaps they feel it’s a limited alliance with a limited purpose, and can be broken off if the purpose at hand changes—safety of the students in Hogwarts.
Even so, I agree that we haven’t seen what exactly the people outside Lucius’s faction and the House of Greengrass got as an inducement to enter the alliance.