TPRS evolved because Blaine Ray considered Stephen Krashen's research into how a second language is acquired fundamental. Today, in certain circles, it's fashionable to pooh-pooh Krashen and his Comprehensible Input hypothesis. At the TESOL conference in Paris I heard one of the main speakers refer to it as the "talk until you drop" method.
First of all, I have read Krashen's five hypotheses and they correspond with my own personal experience as a language learner and as a language teacher for more than fifty years. They match what I have observed and what I have experienced. I have seen no research or arguments that can counter that. If you are not familiar with Krashen's work, there is an excellent summary at http://www.sk.com.br/sk-krash.html
On the other hand, there is research to back up Krashen. There are his own findings, but also that of others. One of these studies that I read recently explains how the subconscious is able to grasp and apply grammatical rules that have not been explained to the students. http://www.cam.ac.uk/research/news/unconscious-language-learning/
This is the goal of TPRS : To present the language so that the subconscious soaks up the structure and spontaneously reproduces correct language. Students in a school system have only a few hundred hours to learn a foreign language. We needed thousands of hours of immersion to learn to speak our native language. It seems logical that class hours should be devoted almost exclusively to concentrated comprehensible input, that any time given to talking about grammar in the native language is wasting our limited time. However fascinating the intricacies of grammar may be, we can not expect young learners to share our fascination. Most young students are excited about learning to communicate in another language. Their excitement and motivation soon die away when confronted with lectures on whether or not the genitive form can be used with inanimate subjects. (Which is a question that not all native speakers agree on.)
I'm constantly trying to find metaphors to explain to students, and their parents, the difference between acquiring a language and learning a language. Acquiring targets the subconscious whereas learning a language targets the conscious mind. I recently used the metaphor of passing a driving test. My daughter-in-law, a very intelligent, hard-working person who was highly motivated, failed her first driving test. She had done nothing very wrong, but the examiner felt that she wasn't ready to drive on her own. She retook the test a few weeks later and passed it. My explanation is that the first time her conscious mind was in control and she was thinking through every action. The examiner saw that she had not yet acquired the automatic reactions that a good driver must have. The second time she was more relaxed because she had decided that if she failed, she would keep trying until she passed it, and she let her subconscious guide her. The examiner saw that she had the spontaneous reflexes she needed.
Stephen Krashen calls the conscious mind that intervenes to tell us how to speak the language our "monitor". The monitor is an editor. It's very effective when we have produced a written text to go over it and correct the mistakes we perceive. It becomes disastrous when we let the monitor take over our spoken language. We hesitate, we repeat ourselves, we stumble, and we get very little out. This happens because we are thinking more about the form than the content. When students concentrate on content and forget form, their language will be as correct as possible, given the input they have received. I've often noticed during oral exams, that a student will say something correctly, stop, think about a grammar rule, and then say it differently and incorrectly. Here the monitor is intervening, hindering correct expression, like a backseat driver who hasn't seen the signs saying no left turn.
"Talk until you drop"? There are teachers doing this. In France teachers are instructed to use the target language exclusively. There's no question that most English language teachers in France speak excellent English and can furnish a good model for their students. They give input, yet their students do not seem to acquire the language. Why? Because they are not trained to make their input comprehensible. I once asked a colleague with a lovely British accent to talk to one of my classes about a subject in which she was far more knowledgeable than I was. She spoke so quickly that even I had difficulty understanding her at times and used her expert's vocabulary. The students soon stopped making any effort to understand her. She was not giving them comprehensible input.
I later asked another person to speak to the class on the same subject. His English was only slightly better than theirs. He spoke slowly and used his own limited vocabulary. The students were hanging on every word because they were understanding him. He was not as good a model as she could have been, but his input was comprehensible. Teachers who talk until they drop without furnishing comprehensible input can not produce fluent speakers. Their example should not be used to refute Krashen's theories.
Many of these teachers will tell you that their students can not follow their grammatical explanations, so that part of the lesson has to be in French. TPRS finds that lengthy grammatical explanations are irrelevant. Grammar is pointed out in "pop-up" questions that take only a few seconds. It's important to note the reversal in the order. Traditional grammar explains a rule, furnishes examples and then drills the mechanism. In TPRS classes students hear the structure many times, and when it has been acquired, the teacher points out how it affects meaning. Because the students have already acquired the structure, it only takes a few seconds to highlight the mechanism. So we have traditional teachers speaking in the TL for most of the lesson, but switching to the native language whenever it's important to be understood. Doesn't that give the message to students that trying to understand is a wasted effort because anything that's really important will be in their native language?