Could you imagine using an implementation of TLS that "probably" authenticated your network traffic though? I think there are two separate reasons we prefer to make strong guarantees in cryptography:
1. That's often really what I need. If I'm downloading e.g. software updates over the network, I really need those to be authentic.
2. Even when I arguably don't need strong authenticity, like just reading some news articles, I want to use the same strong tools, because I don't want to have to study and understand (much less teach) the situations where some weaker tool fails. Inevitably I'll get that wrong or just forget, and I'll end up using the weak tool in some case where I should've used the strong one.
In this case, if I imagine teaching how commit signing works with a weak hash function, it sounds like "Signing commits means that no one can sneak malicious content into your repository, unless they first steal your secret signing key, or else you ever committed (or allowed anyone else to commit) a non-text file that they created." Actually writing that second part out makes it feel really bad to me.