Language discovery

Words follow rules that are sometimes rather mysterious. Today I found the following sentence in one of my students' essays:

[*]This amount isn't possible to eat and isn't possible to produce.

Nevermind what this is about, but I bet you'll agree with me that this sentence is not well-formed.

A small change does the trick though:

This amount is impossible to eat and impossible to produce.

That's kind of weird, isn't it?

My trusty Practical English Grammar doesn't tell my why, but notes that while convenient, dangerous, difficult, easy, hard, impossible, safe, unsafe can be used in the noun + be + adjective + infinitive construction, possible is an exception. Their examples are

This cake is easy to make.
The instructions were hard to follow.
The car isn't safe to drive.

and replacing these adjectives with possible just leads to confusion.

Is it just a question of logic? Is there a reason for this phenomenon? Or is it just a mystery?