I flew from Detroit to Boston a few years back in a 4-seat, single engine airplane after an electrical failure. On a hand-held radio and with no electrics, ATC had a good primary target on me the entire way (at 5-9K feet). On controller handoffs, I would have to turn north for 1 mile for them to confirm the primary target they were looking at was me.
Up and down the Eastern seaboard, I pretty regularly get traffic called out as "primary target only" which also means ATC has no idea of the altitude. Those tend to be low, slow moving aircraft (often without electrical systems).