Given that there were about 20 years between the end of WWI and the beginning of WWII, it's possible that Europe's Founders had a sense of urgency and that they believed that a "cautious" approach would not have worked.

On the other hand, the whole thing started with a very limited and, indeed, "cautious" European Coal and Steel Community. The single market itself was already "mission creep". The "Founders" set a ball rolling and hoped that further integration would be inevitable.

Economics is politics by other means