...allowing the radar system to include the altitude information next to the aircraft's target, as well as receive the transponder code and include some flight plan data next to the altitude information. When a transponder is turned off or not equipped on an aircraft (some GA aircraft do not have transponders), ATC can still pick up the aircraft on primary radar. While a primary radar target does not have the altitude or flight plan information next to it...
The transponder does not provide any flight plan data, at all. The only thing it broadcasts to the radar system is a 4-digit beacon code, and an altitude. Radar automation systems do the rest.
Terminal or Enroute automation systems manage the flight plan data via the NAS HOST computer system, and parts of that data are presented on the radar system for the controller to access. It is true, the radar system cannot display altitude information for a primary target, or one for non-mode C equipped aircraft either. But the datablock will still have exactly the same flight plan information displayed as a transponder-equipped aircraft would because flight plan data is independent of an aircraft's transponder.
And by the way, a primary-only, or non-mode C track in the enroute environment can still display a controller-entered
altitude in the datablock despite the equipment limitations.
A Mode S transponder broadcasts more than a 4-digit beacon code and an altitude. It also broadcasts a unique hex code that can be correlated to the aircraft's N-Number in the FAA database, and is also able to broadcast an 8 character "Flight ID" which can be the N-Number or aircraft callsign, or other string manually entered.