Depends on the child and the activity right?
Personally I often prefer to introduce new activities just at the point where I'd feel comfortable leaving them unsupervised (once they've learned it).
A major goal of parenting is to guide your children to independence. This is a sort of negotiation between you, reality and the child. While it can be heartbreaking when they come to you with injuries, you can't watch them all the time (and it's not healthy to try).
If you introduce an activity "too early" such that you always have to supervise, it has some advantages for child but can quickly become a drain on you (they want to do that $thing again but you have other stuff to do) and they feel less independent because they always need your help to do it.
What our family looks out for a lot is "cliff edges". This is where an activity or situation has a high / unreasonable risk vs benefit, and the harm happens quickly and is surprising. These require special attention. Once kids know where the "cliff edges" are they can explore more safely.