Help needed on an idiom

I am writing this only from my logical sense; I have not read about such explanation anywhere - you need to verify this explanation with another expert.

As I understand, as .... as... is a comparison rather than an idiom.

Moreover, when as is used to compare, a clause must be used.

I am as good as Jack is actually I am as good as Jack is.

Now let us see in details how the comparison works:

The teapot is hot.
The sun is hot.

The teapot is as hot as the sun (is hot).

Now eliminating the unnecessary repeated part from the second element of comparison we get:

The teapot is as hot as the sun.

Now let us take your example and work the reverse way back and see which two elements are compared:

The teapot is as hot as to burn my mouth.

Which two elements are compared? ... let us add back the repeated parts:

The teapot is as hot as (the teapot is) to burn my mouth.

The teapot is hot.
The teapot is to burn my mouth.

The second element does not seem to make much sense, hence probably the comparison is wrong.
However I am not aware if any special idiomatic usage makes the comparison you mentioned valid - after all idioms cannot be explained by any rules - you would require to verify with an authentic grammar book - I searched the bible of English grammar, Wren and Martin, but could not find anything on this topic.