The meaning I want to show with this phrase is that you do something more times and it produces better results. Is "the more often — the better" correct? Or maybe there are any set expressions instead of this?
A common expression suitable here is practice makes perfect.
The more [often], the better and other variants just sound like bad translations to me. They distractingly call to mind the more the merrier, which obviously isn't what's meant.
This is how I would stylize it:
Other phrases that mean similar things: