I notice that I am confused. The impression I have of Leaf, as it has been described various times throughout the story, is that it is a collection of micro-nations in the form of Clans, who only grudgingly surrendered some of their autonomy to the institution of the Hokage and jealously hoards the privileges they still have. More poignantly, these clans are in a state of perpetual paranoia about their clan secrets and successfully enshrined the enforcement of said secrets into the foundational laws of Leaf.
My baseline expectation is that the standard provision for "a member of a clan wishes to leave and share their secrets with another clan, or maybe Leaf at large" is "you are not allowed to do that, and if you try we will kill you". That's how I imagine it worked in the Warring Clans Era, with quite a lot of confidence, and I struggle to see the Clans agreeing to this "Hidden Leaf" project if it meant surrendering that right. After all, any Clan that's made it this far is going to know that bad actors are an inevitability, and that you only survive as a clan by keeping them from inflicting catastrophic damage against you.
So I have a strong expectation that the laws at the formation of Leaf would not include provisions allowing someone to leave a clan without recourse, taking any and all secrets with them free to share with whoever they like. Even accounting for the fact that clans keep their best stuff to inner circles, such people would only have a lower rate of betraying the clan, not zero. The risk would still be immeasurably great, in the eyes of every clan.
Is this a recent thing, with the rise of the KEI? If so, how did it not get demolished by a unified front of clans terrified at the prospect? I struggle to think of a scenario, any scenario, that would get the clans to agree to this situation. Would the Minami have had to fight for their lives against Lord Hyuuga, who used his authority as their Clan Head to demand their deaths without ordinary Leaf law intervening (and only being thwarted by executive action by the Hokage allowing the Minami to form their own clan), if they were permitted to simply leave the Hyuuga whenever they please?
In this same chapter, it is said that getting access to a clan's secrets is one of the main reasons to be adopted in the first place. It would be extremely hard to say that every adopted ninja is properly and fully vetted for loyalty before they are given access to clan secrets (remember that even those raised in the clan will be expected to have some rate of bad actors, let alone outsiders). So, failing that, the only options seem to be "precautions exist to stop said ninja from walking away with the secrets and spreading them" and "any secrets a clan is willing to share with adoptees cannot be expected to remain secret for very long". It is also known adoption was not uncommon even before the events of the quest, when a talented clanless ninja showed promise: the risk profile existed in the past as much as in the present.
Heck, for that matter, if these laws are as Kei said, could you not get people agreeing to adoption with premeditated intention to betray the clan? I suppose at that point you're liable to get a kunai to the neck in a dark alley, but this again stands out to me as a security risk that would make every Leaf clan extremely concerned. Revenge or not, you can't put a secret back in the bag. Forget the KEI not wanting to hand out any adoption tickets, what clan would want to adopt ninjas at all if this is on the table?
Perhaps I'm looking at it the wrong way. Maybe it really is a new innovation, ushered in with the KEI or thereabouts, and the Clans were so shaken up by the debilitating events around then (BotG, Collapse) that they were in no position to argue against it. Maybe there's widespread sentiment against it that simply hasn't boiled over yet. Maybe it's an open secret that, like Mari implied, anyone who tries to leave with clan secrets wouldn't survive the experience no matter what the laws say. But then why have the laws in the first place? It just seems so at odds with everything else we know about how Leaf operates.