A major problem with this is the assumption that Trump would not face any challenges from other Republicans. While Trump won the 2016 nomination, he did so not having won a majority of primary votes (just shy of 45% of all Republican primary votes were cast for Trump). Running simultaneously as a Democrat would split his resources (he would be fighting a political war on two fronts). A politically weak Trump (assuming he doesn't improve his approval ratings by 2020) might lose enough delegates to lose one or both nominations. It's also likely that some of the stronger candidates from 2016 (Marco Rubio, or Ted Cruz) still have enough of their political machines to restart in 2020.
Another problem is that some contests are run as caucuses. These are considerably less straightforward than a regular primary. Consider this quirk of the Iowa caucuses for Democrats
A controversial aspect of the Democratic caucuses is the lack of a secret ballot. That means people will have to live with the vote they cast in front of their friends and neighbors for the next four years. And the faint of heart may be susceptible to pressure from more vociferous contemporaries.
Thus, a candidate who wins the first round of a caucus is not home safe. They can still end up losing if their supporters fail to win over backers of candidates eliminated for not passing the threshold and instead see that support go elsewhere -- one reason why the organization and training of precinct captains is so crucial for campaigns.
It's also why the second choices of voters for a presidential candidate are so important in the Democratic caucuses.
Trump is deeply unpopular with many Democrats. It would be hard to see lots of Democrats publicly voting for him as their party's nominee, especially after what would have likely been 3 years of criticizing him.