Stochastic calculus is the only available tool for proving things about continuous-time stochastic processes. There aren't any alternatives, save guessing at criteria and backtesting them.
Yes, for sure useful for the appropriate mathematics. My point is, the trading strategy was a simple heuristic wrapped into overly complicated definitions and proofs. The complicated mathematics added exactly nothing to the application.
Yes, it was something like that. But "desirable" here means something very different for mathematicians and traders actually applying the strategy (I.e., they don't care at all, and neither does anyone else working in finance).