Hello Mauro ,
I have taken the 3 modules you mention (there are two more now: TKT cal and TKT clil ) 2 years ago and I did because I informed myself about it and found that it was - in my opinion - an objective way of evaluating a teacher �s knowledge OF the language and ABOUT teaching.
In the case of English speaking countries I think it also assesses the teaching part objectively, the fact that English is the native tongue doesn �t have anything to do with how good or bad your teaching skills are. But I wouldn �t know about the part of testing the language in itself, since it �s much easier for you to learn what �s correct in English as the language is all around you !!
You have mentioned everything regarding the exam, I have nothing to add, except maybe that you never actually fail this exam, you get a grade. It �s band 1 to 4 being 4 the best.
Also, each module consists of 80 multiple choice questions to be answered in an hour (I think it was an hour, I don �t know if it has changed).
So, if there is anything else you want to find and I can help, just let me know.
A hug.
Alicia
PS, here �s the link to TKT in case somebody else wants to find out more or see a sample exam.