Ownership has two components: benefits and control. If you both benefit from and control your shares already, it doesn’t matter whose name is on the certificate. Using CeDe just makes it easier to buy and sell shares. Prior to that people had to literally track down physical owners, call them up, and ask to buy their shares. Read Warren Buffett’s biography (“The Snowball”). He did it all the time.
Your home address has your state and country on it. Do they “own” your house in any sense of the word? Their name is on it and you pay them for services for your property. They make rules you have to follow. No, they don’t own your house but they do have a responsibility to provide services for it. Should you leave society and set up your own water, septic tank, power, etc.? You can but it’s not easier and it doesn’t affect the ownership of your property. Same with direct registration.