2004President George Bush (R-TX) / National Security Advisor Condoleezza Rice (R-AL) ✓
Senator John Edwards (D-NC) / Senator Evan Bayh (D-IN)
A constitutional amendment is passed prohibiting candidates from holding office in the executive branch if over 60 at the time of their election, somehow. Wouldn't happen but whatever. Bush runs because he would be allowed to finish his term, but Cheney's out. In the Democrats' primaries, Edwards narrowly beats Clark, who would just barely make the cut for one term anyway.
2008Fmr. Governor Mike Huckabee (R-AR) / Governor Tim Pawlenty (R-MN)
Senator Barack Obama (D-IL) / Senator Tim Kaine (D-VA) ✓
2012President Barack Obama (D-IL) / Vice President Tim Kaine (D-VA) ✓
Senator Rick Santorum (R-PA) / Congressman Paul Ryan (R-WI)
2016HUD Secretary Julián Castro (D-TX) / Senator Kirsten Gillibrand (D-NY)
Senator Marco Rubio (R-FL) / Governor Scott Walker (R-WI) ✓
In a vacuum, "the next Obama" runs. IMO this is the point where we'd more realistically get some fairly unknown people as candidates because both parties- especially the Democrats- would be more conscious of keeping a stronger bench of young people.
2020President Marco Rubio (R-FL) / Vice President Scott Walker (R-WI)
Mayor Pete Buttigieg (D-IN) / Fmr. National Security Advisor Susan Rice (D-DC) ✓
Buttigieg picks Rice because unlike Harris, she would just barely make the cut to run with him again in 2024. The enthusiasm for Rubio runs out as anti-maskers turn on him.