Because it is incorrect English. They had/have gone, they went. Went doesn't take have.
I believe you, but can you say what type of English is native to you? In standard white middle-class home-counties British English it's wrong. But English has many flavours, none better or worse than any other.
Yeah. Using the past tense form instead of the past participle form is one of my pet peeves. It has been a marker for a less educated version of English since at least the time of Dickens. However, given that I'm now hearing it regularly (have came, have went, etc.) on news shows, I suspect that this is something that is changing in the English language. In the mean time, in WRITTEN English, it is a marker of a poor education. Definitely not something you want to teach ESL learners, and these courses are often used by non-native speakers to both learn a new language and to improve their English.