In all of the resources I use (incl Genki, A Dictionary of Basic Japanese Grammar, various websites), the
～ほうがいい construction is nearly universally translated "had better ~" and rarely includes the word "should ~". This is while noting that
～ほうがいい is a polite suggestion. Nearly all example sentences I find use the translation "had better ~".
As a native speaker of English (Eastern Canada), the phrase "You'd better ~" rings quite assertive and somewhat condescending, and in polite speech I would rarely elect to use that phrase over "should". In fact, "You'd better ~" would be reserved for people I was familiar and casual with.
Is it wrong to translate the phrase
～ほうがいい as "should" in the typical case, or to use it where I would use "should" in English?