Don't know about any specific age, but if you ever intend to move in with someone other than your family, it's a very good idea to have tried living alone first.

Yes, incompetency and responsibility are issues. There's a lot of stuff to be done in a house/home. Since you already live with someone, there's a high chance that they're doing something that you either don't know about, or don't know how to, because they're the ones doing it. Living alone will inevitably teach you how to do everything and also let you experiment with how you want it done.

In that process you'll also learn that there are probably things that your family does differently from what you want. Perhaps they have arguments over stupid stuff, or they are happy living in more mess than you prefer, or they wash all the clothes on the wrong temperature (horrible, I know). As stupid as it might be, small stuff like that is important if you want to live with someone else.

You know how some motivational memes say "if you can't love yourself, how can you expect others to love you". Same thing applies to living with others: "If you can't live by yourself, how can you expect to live there with someone else?"

Financially it doesn't make sense at all, but in my opinion, living alone is a necessary thing to do before committing to living with a partner. At least for two years or so, and the twenties are usually a good time to do so, because you have fewer obligations and your family can still help you out if everything fails.