As a pilot, it's valuable to be able to see tail numbers to help correlate what I'm hearing on the radio with what I'm seeing on my displays. I can guess who's who from position reports, but seeing the tail number leaves no ambiguity.
There are also some smaller facilities that use ADS-B to monitor traffic, but aren't networked into the national ATC radar system.
Aviation events will also setup their own temporary control tower, and frequently use ADS-B as an aid for sequencing traffic. (Again, without access to the national ATC radar network.)
For folks who need privacy, there are a couple options that already exist - UAT privacy mode or private Mode S addresses. Though notably, both of these are only available options for domestic flight within the US.
Why? They are using our airspace. Looking down in to our backyards. I have a right to at least get an identifier I can use to report to authorities.
I've worked with VVIP executive protection teams before and if the trip needs to be secret they will schedule plane swaps along the trip or rent a jet that is not attributable to the company.
Having to coordinate with every ATC jurisdiction along a flight path would be extra work and leave room for errors.
Additionally it wouldn’t work for flights that don’t have a planned route, like a civil aviation pilot who’s just cruising.
It’s akin to having a license plate on your car.
I'm not sure how well that would work w/r/t ATC hand-off and their ability to look up flight plans.
Furthermore, there's the problem of getting the random ID to ATC after the plane has "started up."
That wouldn't stop any traffic collision or ATC function from working but would prevent persistent tracking of for example private jets.