First things first, how can you read from a file that doesn't exist? Even you questioned that later, so this is a strange question. – Do you mean if you try to open a file that doesn't exist? nil would be a reasonable value. It is how Go signifies the absence of something. nil is always useful and with `if file == nil` will tell you that the file isn't there. No need to observe the error.
If you need to know why the file isn't there then, sure, you're also going to have to look at the error. Sometimes that is important. In the case of opening a file you realistically will need to know why it failed to open so that you can resolve the condition, but in other cases you don't need to worry about why it failed. Checking the error would be unnecessary in those cases, assuming the function author has some understanding of how to make even half-decent APIs.
Let's assume here, for the sake of discussion, that you have no need to know why the file was unable to opened. Again, how do you envision garbage propagating into the rest of your program?
But also, let's say the read function in question is named ReadInt32. Then what does it return on error?