Well, because you can't. This is like asking why the word for "dog" isn't "grup". It just isn't, and thinking there might be a reason is an error. That's not how language works. But in a different world, the word for "dog" might be different.
"Let us have a cup of tea" isn't something that anyone would say (outside of a demand for permission), and if you say it, at best you'll get very funny looks.
Here's what CGEL has to say (page 935):
> Syntactically, this construction indicates that the specialisation of let has been taken a significant step further. The 's here is not replaceable by us [...] It seems clear, rather, that let and 's have fused syntactically as well as phonologically, and are no longer analysable as verb + object: they form a single word which functions as marker of the 1st person inclusive imperative construction.
Not at all a nonsense word situation, as you said above, though. Also not sure I would say cgel > oed for authoritative sources of meanings of words in English... But you do you.
> Not at all a nonsense word situation, as you said above, though.
Where did I say that?
> Also not sure I would say cgel > oed for authoritative sources of meanings of words in English... But you do you.
There are a couple of problems with this:
- CGEL is not a source for the meaning of words; it's a description of the grammar of English. But that's fine here, because "how many words is let's?" is a grammatical question.
- The OED is a source for the meaning of words, making it a bad choice for grammatical questions, which are tangential to its purpose.
- The OED also deals extensively with the historical usage of words, even when that usage is not possible in the modern language. You have to be careful.
- You haven't cited the OED. Your link goes to the unrelated "Oxford Learner's Dictionaries". The OED is at least a name with immense prestige; the Oxford Learner's Dictionaries is not at all the same thing.
