Or actually not really - there's been way too much politicization of DoJ decisions, their decisions shouldn't be based on politics, so yes, they should prosecute. Fiat justitia ruat caelum, and all that. And of course a jury of the people would be able to actually vote their conscience, unlike most Republicans in the Senate in the impeachment.
But whether that will actually work out for the best for the country as a whole, that's a lot less obvious. Slowly but surely, Trump does seem to be losing ground at last, though it doesn't look like he's losing it fast enough to fail to win a Republican primary in '24. And if he runs, I'm far from convinced that he can't win - even win fair and square, without needing any of the cheating the Republicans are gearing up to do on his behalf. With yet another trial making things all about him, that makes it easier for him to maintain his grip - and probably pushes him to announce his campaign even earlier, so as to undermine the legitimacy of the prosecution in the eyes of his supporters even more. And considering the endless appeals that are sure to follow, it seems basically impossible to actually have him in jail and take him out of the running before the presidential election - even assuming he does end up in jail and doesn't get somehow bailed out by the SC. Though I dare say he would find his appointed justices on the SC a lot less biased towards him than he might like to think.