I don't agree with your point.
Leaving in debug code, especially for an entire part of the launch that doesn't exist anymore by bringing in reused and untested code, seems like the real problem. I'm pretty sure integer overflow in this case would be undefined behavior, so you don't know what the compiler would do, especially since things were a lot more wild on the hardware side in 1996. Your point sounds like arguing that preferring Objective-C would prevent all those pesky `NullPointerException`s in Java since it allows sending messages to nil (null), but that's success by coincidence.
If you read the ESA's report [1], there were a lot of things which failed before you even get to the language. This software failure is the only one in the entire Ariane series of rockets. Considering that this is 1996, the list of languages to pick from was pretty slim, e.g. this predates C++ initial standardization (1998), `enum class` and other modern C++ features.
Even using just Ada 83 (of which 95, 2005, 2012, and 2022 succeeded and improved), I would argue that its forward looking features of preventing mixed mode arithmetic having properly typed checked enums and other features (like being strong typed) probably prevented a significant number of failures should other available languages at the time been used.
[1]: http://sunnyday.mit.edu/nasa-class/Ariane5-report.html