I agree, but a lot of other languages handle this much better. In Rust (predictably!) you receive a Result type, and if you don't want to check the error you either .unwrap() it or apply the ? operator to pass it up.
I feel like making "let's not check this error" explicit rather than implicit would be an improvement. Currently in Go it's impossible to tell whether someone forgot to check an error, or if they omitted the check intentionally.
As an aside: I feel like if you are ever in a situation in which fmt.Println returns an error, then whatever situation you are in is already far, far beyond saving. Maybe fmt.Println should just panic on an error, that seems better than output silently being dropped!