Your job as a teacher when working on pronunciation is similar to that of a gymnastics coach. You don’t need to demonstrate the exercises yourself, but you do need to understand what your students have to do and help them to do it.
In the PronSci approach, the teacher brings her students to a point where they are sensitive to what they are doing in their mouths. They learn how to make the sounds of English that are unfamiliar to them, how to combine these sounds with others to create words, and how to combine words into fluent sentences, spoken at different speeds with authentic melody and stress.
To stop students from trying to 'Listen & Repeat', a teacher should stay largely silent. Charts enable her to do this because she can refer to sounds, words, etc, using a pointer, without having to say them out aloud.
Pronunciation is best worked on in two phases: (1) concentrated work to put the basis of the system into place and (2) ongoing work. Since pronunciation takes time to be mastered, the ongoing work is essential; it is done 'in the moment', alongside grammar, vocabulary, etc. Pronunciation is worked on in micro-lessons which may last for a few seconds or take a minute or two.
Having the PronSci charts on the wall means that they can be used whenever a pronunciation question or problem comes up in class:
Getting both stress and reduction right is crucial to what is generally called 'rhythm'. (In English, stressed syllables are made more prominent by reducing the syllables around them.)
'Listen & Repeat' doesn't give students an entry into the problem of English rhythm because most students either don't hear the reduced syllables or don't hear them as being reduced. And when asked to use such syllables, students don't know how to articulate them properly.
In the PronSci approach, the physical movements needed to produce reduced sounds are taught explicitly. And the stress and reduction system has been 'built into' the charts so students become aware of it from the start.
When an English speaking child is learning to speak, creating stressed syllables is a physical activity. He has to make greater effort with the expiratory muscles of his respiratory system.
In 'Listen & Repeat', students are asked to copy stressed syllables by speaking louder. In the PronSci approach, students learn the correct physical movements to create prominent, stressed syllables.
English speakers hold their tongues in a completely different way from the speakers of most other languages. This is part of the 'articulatory setting' of the language, and when learners adopt it, their spoken English improves dramatically. If students remain with their L1 articulatory setting, they will always struggle to pronounce English well.
There is no place for working on the English articulatory setting in 'Listen & Repeat', but it is at the heart of the PronSci approach.
A large part of listening is about having the right expectations about what you are likely to hear. If students don't appreciate how native speakers pronounce English, they will probably have comprehension problems.
The best way to deal with this is for students to learn to produce English more authentically: better pronunciation helps to improve listening.