By CLT I assume you mean communicative language? I certainly try to get my students communicating as much as possible and as naturally as possible in the classroom, much to the chagrin of my Chinese colleagues, who would rather spend the majority of class time trying to hammer grammar rules and phonics sounds into their little heads. 

I suspect it comes down to two things, neither of which are really related to whether taking a purely communicative approach is actually more objectively effective than any other approach.

1. It's much easier for teachers to see direct results when they teach communicatively i.e., if you teach them a few stock phrases each lesson and they can use those phrases at the end of the lesson, that feels like a success.

2. A lot of the native speaker teachers working here in China have minimal or no formal training. I imagine that it's much easier to tell a completely green teacher "just get them talking" than to try and give them a crash course in language learning/teaching theories.  

For myself, as I said above, I am very much in favour of getting my students to communicate naturally as much as possible, but I'm not convinced that merely having students taught 'oral' English, with no structural understanding (grammar) or literacy to back this up is enough. 

What works well, also depends on the group of learners; at the moment I have young students, and they respond best to (i.e. pretty much only respond to) TPR activities. When I taught teenagers (NEVER AGAIN), they got an awful lot of task based learning, because that's pretty much the only thing they responded to.  

Sorry i saw an i before the t my answer will not make sense now.....