I agree it's helpful to say and that "I'm sorry" does mean the thing I said in certain contexts. And that people can appreciate it as such. Just that it's definitely an expression being expanded based on need and there are folk who struggle with words meaning different things in different contexts.

Like most people first learn "I'm sorry" to mean "I acknowledge my responsibility in your misfortune and regret my actions" and later learn it also means general condolences and empathy, which is a separate use case. For some people it's no issue but others find the double meaning uncomfortable.