If those places such as Binance or other reputable exchanges or casinos or whatever can be trusted, I think we do not have to feel worried if we want to do KYC because they will make sure to give protection for their customer's data.
But in another case, when those people have a big asset but want to hide from sending documents for KYC, they will search for the other way that can help them get the fiat without verification.
But if they only want to hold the coin without having an intention to sell, they do not have to bother searching for the site that does not apply KYC or apply KYC.
But they can use their coins to buy something out there but still, they need an address to receive the product, which means they are still giving their data to the site unless they use a fake address or PO BOX.
I would say if you want to just hold the coin and not give any KYC to anywhere, just use the coins wallet and not an exchange, even a hardware wallet would be more than enough to be fair. I have some wallets on my pc, and saved all the possible backups on paper and on an USB as well.
I have a few of my coins and tokens there, it makes sense because I do not need to really deal with exchanges or anything like that and my computer is as safe as it gets compared to a multi-billion dollar company.
Not because they have worse security than me, they have 100000x better security than me but nobody cares about me and my small few bucks which wouldn't even worth getting hacked whereas binance or other big places are getting attacked constantly and they are just good at defending, the moment they fail to defend would be the moment they crash as well.
You are absolutely right.
We can follow your step to secure our coins and not store our coins in the exchange, especially if we want to avoid KYC, which will be a nightmare if the exchange gets hacked.
I remember a story from my friends. He has an old smartphone but he installed multi-wallet apps to store some of his coins and suddenly, that smartphone is on somewhere he does not know.
He realizes that and yells that the smartphone is worth billions of dollars, although the real price of that smartphone is just less than $200.
Short story, he found his smartphone in his safety box and he forgot that he moved his smartphone on that box last night hahaha.
It is better to use apps that have an exchange inside the wallet so we do not have to send the coins to any exchange and only send to the exchange if we want to withdraw the funds.