Learn English – How might one rewrite interrogative sentences with contractions, such as “Why can’t we … “, more elegantly

The transition point was about a century ago

Note that if we substitute a pronoun (I, he, they) for "why", the transition point comes much later (1980 for "I") – or hasn't even happened yet (all other pronouns). I can't explain why that is, except by pointing out that this very sentence is an increasingly typical usage. Maybe we all tend to be a bit less formal when introducing our own selves into the text.

It's only my opinion, but I think can't (similarly, let's) are examples of grammaticalisation. The contracted form has effectively taken on a "life of its own", leading to a situation where OP is prepared to accept that there may be contexts where can't is "grammatical", but "cannot" (or the equivalent "can not") wouldn't be valid.

Using cannot / can not might be a bit stilted in many contexts now we're so used to seeing the contracted form, but I don't think it's ever ungrammatical.

It appears that the contracted form of ‘let us’, let's has acquired idiomatic meaning and usage through the years.

Let's go and let us go, may convey different meanings. Let us go in the sense of allow us to go, may not be replaced with let's.

Let's see why:

Usage note:

• Let’s is always inclusive, which refers to both the speaker and the addressee, while let us is commonly exclusive, which refers only to the speaker. (www.yourdictionary.com)

  • Let's go, we are late. - inclusive we
  • Release us and let us go! - exclusive we

According to the following source:

• Merriam-Webster’s Dictionary of English Usage - describes the construction as idiomatic and has this to say: “Let’s can also be followed by a pair of pronouns in either the nominative or the objective case; the constructions occur in both American and British English.”
  and it notes that these “are idiomatic constructions—no matter what the case of the pronoun—found almost exclusively in spoken English.”

  • Some grammarians believe that “let’s” is treated here as a single unit rather than a contraction of “let us”—that is to say, the “us” is swallowed up. Consequently, the speaker senses that “let’s” needs some propping up, and adds “you and me” or the slightly more formal-sounding “you and I.”

  • A modern grammarian might say that “us” or ’s has been “desemanticized” or has experienced “semantic loss,” and thus requires additional information in the way of “lexical support.”

  • It’s been argued now and then that because the object pronoun “us” is part of the contraction, any propping up should be done with pronouns in a similar case. By this argument, “let’s you and me” is preferable to “let’s you and I.”

  • But in our opinion, that argument merely creates the illusion that “correctness” is possible (or even desirable) here. As the OED says, this is an “irregular phrase” no matter what the case.

(www.grammarphobia.com)

Etymology:

• Merriam-webster says that the first known use of let's, a contraction of let us, dates back to 1567.

• The contraction “let’s” has been around since at least as far back as Elizabethan times. Shakespeare used it hundreds of times in his plays, including King Henry VI, Part II, with its famous line:

• “The first thing we do, let’s kill all the lawyers.”

• As to why the contraction is used with let and not with give or take for instance, I think that let's (as encouragement or as exhortation) is such a specific, often used, and natural expression whose common use has probably contributed to its diffusion.