It can be pretty convenient to throw an error and be done with it. I think for some languages like Python, that is pretty much a prefered way to deal with things.
But the entire point of Rust and Result is as you say, to handle the places were things go wrong. To force you to make a choice of what should happen in the error path. It both forces you to see problems you may not be aware of, and handle issues in ways that may not stop the entire execution of your function. And after handling the Result in those cases, you know that beyond that point you are always in a good state. Like most things in Rust, that may involve making decisions about using Result and Option in your structs/functions, and designing your program in ways that force correct use… but that a now problem instead of a later problem when it comes up during runtime.
But nothing is forcing you to check exeptions in most languages, right?
While not checking for exceptions and .unwrap() are pretty much the same, the first one is something you get by not doing anything extra while the latter is entirely a choice that has to be made. I think that is what makes the difference, and in similar ways why for example nullable enabled project in C# is desired over one that is not. You HAVE to check for null, or you can CHOOSE to assume it is not by trying to use the value directly. To me it makes a difference that we can accidentally forget about a possible exception or if we can choose to ignore it. Because problems dealt with early at compile time, are generally better than those that happen at runtime.