Sometimes taking on a new accent can be really difficult psychologically for people, even if they can do it mechanically. I suggest to my clients that by using standard American intonation patterns, they are actually portraying themselves in a more authentic way, but many clients see this as “acting” or taking on a new personality and they are resistant to it.
People who speak English with very little inflection, or very little use of pitch changes to indicate stress are often seen as un-enthusiastic, un-engaged, and un-interested in life. These un-s are all negative attributes in our society. In the native languages of many non-native speakers of English, lots of inflection or pitch changes to indicate stress would sound ridiculous, so these speakers carry that mindset into speaking English.
An exercise I have such clients attempt is to go into a coffee shop and order a cup of coffee using (what they perceive as) exaggerated pitch and intonation. I ask them to think about the reaction they got from the person behind the counter and if it was different from the reaction they normally get. It usually is — much more positive and friendly.
But getting clients to remember that and to maintain their mindfulness about intonation is often a challenge.