1. Tony lapses into the bottle and Rhodey takes over as Iron Man. Tony recovers, builds a new suit and returns as Iron Man but Rhodey would also still suit up at times. Then Rhodey nearly gets fried in the damaged armor, refuses to suit up again (can't blame him for that) but still serves as a support character for years until Tony builds the WAR MACHINE.
2. Hal Jordan resigns as GL, John Stewart takes over. At the end of the Crisis HAL is a GL again, but John doesn't get retired. At least not until Sinestro caused the implosion of the CPB until the Guardians later returned to repair it.
3. John walker takes over as the 5th Captain America. Rogers eventually reclaims his identity and Walker becomes the US Agent
4. Danny Ketch is the GR of the 90's but Blaze shows up first as hunter then supporter. Then years later Blaze is GR again and Danny is shoved aside (boo!)
5. Ben Reilly would have likely stuck around after the Clone Saga 2 ended, but they wanted to definitely show he was the clone and the best proof is to have him crumble to ash after being mortally wounded.
6. Eric Masterson took over as THOR on Earth with THOR's blessing until ODIN intervened and gave Masterson the Thunderstrike mace instead.
Yes, but serving as a supporting character really isn't sticking around, and does nothing to solve the problem that needs to be addressed.