I think this is a red herring. There wasn't time to run a new primary. That ship sailed the moment Biden ran for re-election, because no serious Dem challenger was going to oppose him. Once he stepped aside, Harris was the best option realistically available given the time frame. And she made was was going to be a blowout loss fairly close.
The only chance for someone other than Biden or Harris to be the Democratic nominee was for Biden to announce well in advance of the primary that he wasn't going to run again. Then you might have seen the Newsom, Shapiro, Klobuchar, Harris, Buttigieg matchup battling out for the party's top spot.