The democrat convention is in August. If Biden steps down before then, his delegates that he won in the democrat primaries (some 4,000 at the moment) would be free to vote for whoever they want at the convention. That means a big fight on the convention floor that the party does not want. So - to avoid that, Biden doesn't step down until after the convention is over and he is the nominee. And THAT leaves the issue up to the 435 members on Democratic National Committee to pick whoever they want as their choice to run in Biden's place. This is a much cleaner way to eliminate the Biden problem for them, and it ain't their fault that Biden dropped out, right?
But, can they get the new person's name on the ballot? Don't know. But the thing is, whoever they pick will get a lot of votes because he/she ain't Trump. Maybe it really doesn't matter who it ultimately is, there are a good many people who will vote against Trump no matter who the other person is. Would it be likely that the democrat beats Trump? Maybe not, but Biden sure as hell won't.