A big part of the job of safety critical development is knowing the difference between box checking best practices/regulations and building actually safe systems so you can do both.
The complete solution depends on the application and the integrity level. It's not one size fits all, but rather about producing documentation showing you've considered various failure modes and developed mitigations for them (or otherwise accept the risk). Sometimes that's binary analysis of the compiled output to ensure it meets some formal model, sometimes that's a formally proven, decent compiler like concert, and so on.
An additional wrinkle is that the business model for high integrity compilers can also be a huge obstacle here. Some charge seats by how many people have modified the code that's running through the compiler. These aren't cheap licenses either, so companies have a large incentive not to use methodologies that require many eyes making all bugs shallow. There are also issues running these compilers in CI. They might require online license verification on every file, for example, or not allow ephemeral licensing at all.
But also I don’t work directly in these industries and so maybe my impression of this aspect of their processes is incorrect.
IMNSHO the standards were set so low so that C++ could clamber over the low bar, and it's a happy consequence in some sense that Rust has no trouble clearing it, but the bar should be raised considerably instead. Software crucial to the safe operation of an airliner ought to be proven correct, not just slapped together in any of the general purpose languages, including Rust and then subject to a bit more process than for a web app.
Why would the resulting safety improvements be "marginal" ?
It is also ass-covering by demonstrating you followed "industry standard procedure". If you do something different, even if it is quantifiably better, it might make for a stressful deposition explaining why the worse but standard approach wasn't used instead.