Sure it's possible in theory, but how many C codebases actually use formal verification? I don't think I've seen a single one. Git certainly doesn't do anything like that.
I have occasionally used CBMC for isolated functions, but that must already put me in the top 0.1% of formal verification users.
It's not used more because it is unknown, not because it is difficult to use or that it is impractical.
I've written several libraries and several services now that have 100% coverage via CBMC. I'm quite experienced with C development and with secure development, and reaching this point always finds a handful of potentially exploitable errors I would have missed. The development overhead of reaching this point is about the same as the overhead of getting to 80% unit test coverage using traditional test automation.