Why would they do this? Well, once Harris is sworn in as VP and the two new Georgia senators take their seats, the Democrats control the Senate, and the first things they may want to do is get Biden's cabinet appointees approved. An impeachment would take precedence over that, and the Republicans might decide to gum up the procedural works in order to delay those cabinet appointments and other things the Democrats want to do immediately. It does appear that you can impeach someone after they've left office, so the Democrats could wait until they've done the most pressing things, then start the impeachment trial. They might even be able to scratch up the 17 Republican Senators they would need to convict.
What's the point of a post-service impeachment trial? Well, it would first of all bar Trump from ever holding office again. Second, it would strip him of all of his retired-Presidential perks, which are quite substantial, and given that there's a lot of rumors that he's actually broke, he may need them. And finally, it would remove just about any shield at all from him being prosecuted for any state-level crimes. Finally, it might just prove to the rest of the world that the USA has not lost its collective mind the way it may appear right now.
We can but hope that sanity returns eventually. I live in Trump country, and I wonder what the Trumpistas are going to do. They've been relatively quiet these past few days, but there are still Trump flags flying from houses around here.