Cryptocurrency payment gateways on the other hand, use decentralized blockchain technology to process transactions, which provides a higher level of security and privacy.
I'm not sure what makes you come to this conclusion. A payment gateway can still record users' data even if they use blockchain to process the transfer. For example, stuff like e-mail address, user address, volume/transaction history, etc. Do you think they also dump those data to the blockchain or something? Unless the seller is generous and uses an open-source gateway that automatically deletes buyers' info after a few days or something.
Additionally, cryptocurrency transactions are often anonymous, which can protect users from potential fraud and identity theft.
Unless you use some privacy coins, most crypto transactions provide you with pseudonymity at best. That's why services like mixer or coinjoin exist. This also doesn't solve the identity theft or fraud that you mentioned, at best it helps you get fewer phishing e-mails. If you are afraid of fraud or identity theft, the best thing that you can do is stop using a sketchy platform that asks you to KYC for everything you do. You might want to explain more if you really believe this is the case so that we can discuss it better.