Money laundering mostly stops by wagering requirements. Casino KYC you if they have doubts in your honesty. Unfortunately, such doubts they have if you begin to win. And they have no any doubts when you deposit money.
On one hand - there is nothing to be afraid in KYC. On the other hand - today KYC is used mostly against gamblers, not for its real purpose.
The reason why most person are all very serious about their KYC is because most of the time some casino do sell it out but although some of the casino that do that are the ones with no reputation at all but even at that many gambler are still very conscious of the data they do submit to the casino. But like you said there is actually no need to panic if you are clear beside it's a matter of seconds or minute for the verification of the details you submit for reputable casino.
I understand the challenge with submitting KYC to untrusted platforms but the truth is that the advantages of playing in a casino that request for KYC during registration is higher than those that does not require KYC but might turn around to ask for it when there is heavy winning. That attitude is a sign of irresponsibility wrapped under criminal intentions. There have been countless cases of people losing significant income due to casinos requesting KYC after winning; I consider this a deliberate attempt to steal people's fund.
I see the "untrusted" remark to be a reason for a restraint, any casino you do not have a high degree of trust in should not be considered for registering not to mention submitting your details and documents with them. This is especially the new ones that are just sprouting up like mushrooms and the old ones that are not reputable with too many complaints by people.
People are victims of data leaks daily and most of them will never be known by the victims. They may just be leaked for some purposes, especially for email and phone numbers where you might not know it's from them. In rare cases, some bad actors may find a way to clone the passport ID of another simply because they are privy to their data, we've heard and read enough of the risks associated with this KYC. Unfortunately, there is nothing we can do about it, it's the government and the casinos that are cutting the shot here.
The saddest part is that the government that mandated it is not proactively responsible for its proper regulation under some strict conditions. They might build a bridge where any government-approved casinos will not get the data directly but from the government data bank. The casino platform will only be a bridge to accept it while the government do the verification and gives the casino the signal whether it is verified or not. This will reduce data falling into the wrong hands.