I have a few points regarding this.
- Any dubbed content is stripped of basically all cultural interaction, it's just pure language. You're going to miss out on all the body language, gestures, concepts unique to the country. In dubs actors say things that native speakers would rarely say if it was just a regular movie in your target language.
- In dubbed content you learn about foreign countries where people don't speak your target language. You're investing your time in irrelevant cultures when you could be learning more about your target language's culture.
- It's pretty hard to find dubbed content compared to native content in case of Japanese. There are sites with dubbed American movies, but their libraries are rather small.
- Japanese has an abundance of native content. There's absolutely no need to substitute it with dubbed content. I imagine it's not a problem for other languages either, unless we're talking about languages that are spoken in poor countries that can't make a lot of their own content. For example, I was surprised how many television dramas exist in Russian, probably even more than in Japanese, and they make new ones every month.
Taking all this into account, dubbed content is not as good as native content. I advise you limit how much you use it in your immersion. But keep in mind that real Japanese people watch dubs. They know about the most popular American movies, for example. It can be fun.