Collapses are rare indeed, but they do happen. Cf. the collapse of the Italian School of Algebraic Geometry [1], the cleanup of which took all the efforts of Grothendieck et al.
Great example. Weil is said to be the one who was deeply immersed in both the geometric tradition of the Italians and the functional perspective of Riemann, so he was in a unique position to see many analogies and deep connections. (He proved small pieces of it, and laid the roadmap for Grothendieck.) These are the kind of “ideas and understanding” that Schulman is talking about.
What collapsed were the proofs, and some if not all of the ideas survived and got painted over with the new language. Sadly algebraic geometry has this bad reputation of being obtuse and opaque, that it has become devoid of geometry. Mathematics need to be more open about ideas that are not rigorous, not just left unspoken between the experts themselves.
[1] https://en.wikipedia.org/wiki/Italian_school_of_algebraic_ge...