[esafak]

Abbreviation does change it; it narrows the meaning. "Let's go" never means "you should let us go" and "let's pray" never means "you should let us pray".

@ninkendo shared an insightful video below about it. https://en.wikipedia.org/wiki/Clitic

[efdee]

Nowhere does anyone claim that "let's go" means "you should let us go". The discussion was whether "let us go" automatically means "you should let us go", which it does not.