Let me start by concuring with you that accent is a skill that can be taught and learned. With proper training and ample of practice, Americans can no doubt speak Queen's English and vice versa. In fact, American accent is very mechanical. There are actually fixed rules on speech meter and rhythm. Speakers of American English, regardless of what "dialect" they use, tend to follow those rules closely. Furthermore, the so-call rule is quite simple. Stress the nouns. If there is no nouns, stress the adjactives. Verbs would be the lowest in priority. Break long sentences into smaller unit with slight pauses in-between. This is not meant to be comprehensive, but the number of rules are quite limited in American English accent.
Yes, accent can be taught to ESL students. I don't believe anyone can dispute that point. The question is, WHO has the ability to teach accent to ESL students? The majority of ESL teachers have little understanding in prosody. They are trained to teach proper grammar and pronounciation, basic skills that many native English speakers have already picked up in their childhood. Only a handful of ESL teachers are actually linguists!
In order to bring accent training in ESL classrooms, all ESL teachers will need to be retrained. They will have to learn unfamilar theories and new skills in order to teach accent properly. Needless to say, this represents a huge investment. For public school, nothing short of a revolution can bring about such change.
I really like your vision of a "full-coverage" ESL education. May be one day ESL students will receive training in all aspects of the language: Grammar, usage (both formal and colliquial), pronounciation, prosody, and poetry.