No it doesn't. Japan has a standardized mass transit fare payment system, covering close enough to the entire country, and you can get in on that with a card purchased, and topped up, completely anonymously in cash.
Your options are, travel anonymously, and pay more or risk losing the money on your fare card due to them just deciding not work anymore, loss etc. I've gone through 4 now in about three years. Two just stopped working and i lost two. They also don't give your $6 deposit back, so i've now spent an extra $24 i'll never get back, for nothing on top of the money i lost on the first two cards. I've registered them since.
Or
Get tracked constantly any and everywhere you go on transit.
Counterpoint: No it won't, necessarily. I've never had an issue with one of these IC cards (edit: in over 10 years of using them). I've lost one, that's it. I've lost more of the paper tickets _inside_ the station than that.
Do you have actual data on the failure rates of IC cards?
It's anonymous at point of top-up, that's true. But when the card is issued, an ID should be shown.
You _can_ add your name to them if you want. You don't have to.