I don't have a problem with the Bourbakists doing very abstract and rigorous Math. After all, Math was an edifice built on quicksand until they came along. I think they contributed a lot.

However, I also think the Bourbakists created a monster, which was this notion that the "Greek method" was the only valid one, and that the "Babylonian method" was to be avoided. Even Combinatorics was considered "unworthy" of great minds. All geometrical intuition was frowned upon. Applications were laughed at. All of a sudden, Math became sterile. Interestingly, Turing's work, in a sense, derived from Hilbert's program to make the foundations of Math solid. The fact that Theoretical CS exists outside of traditional Math is nothing more than an historical accident. Computability is pure Math. Computational Complexity is still a bit "dirty" but it's also rather fundamental.