I used to feel the same. But in reality, we prove our identity daily - every credit card transaction, banking, electronic tolling, bill payment, health care visit, tax payment, legal proceeding, employment opportunity, voter registration …
What protects us from invasive search is not lack of a uniformly accessible system for identification - its due process. And if the government chooses to compel you against your will and without due process - whether or not you have a laminated ID in your pocket will be irrelevant.
Most of those are optional. You can use cash, you don't need a bank account, nor electronic tolling, or bill payment, emergency room visits are free and there's free clinics. Other various things like legal proceedings, voter reg, and taxes are not things that are "tracked", that's just basic citizenship requirements.
A national ID would make the few cases where you need to hide your identity (like you're a 10 year old girl who was raped and needs an abortion, or the doctor that needs to perform it - https://www.seattletimes.com/nation-world/10-year-old-rape-v...) much harder. Until our government decides not to be so fucking crazy, we need to push back on its ability to unjustly track and then punish its citizens.
What protects us from invasive search is not lack of a uniformly accessible system for identification - its due process. And if the government chooses to compel you against your will and without due process - whether or not you have a laminated ID in your pocket will be irrelevant.