Is there a danger in KYC, in terms of the company you KYC with getting their data stolen? I do not mind KYC, but am concerned about the company having personal data and wallet addresses, or am I over thinking this?
This happens and is a pretty normal thing to worry about. Services like exchanges could also use third party services to process your information so it's safe to say there could be more entities involved.
I suggest at least looking into kycnot.me for exchanges with lax kyc to no-kyc policies. But depending on your planned use cases, you may need to succumb to identity verification for it. IDK what are your planned use-cases but my advise is to weigh things down -- decide for pros you absolutely need and cons that are bearable for you.
Usually exchanges, uses third party to handle their verification and the whole holding of our personal data, we don't know what's the deal with them though, but for sure there are legal bounds that if the third party leaks the personal information of a top tier exchange customer or any exchanges for that matter, they will have to pay big sums of money because that is not acceptable.
I do agree, if you don't what your personal data leaking, then don't submit any or not used centralized exchanges. Instead uses another option, but it not going to be as smooth as a CEX can do as far as experience goes, but at least we have a choice.