My take regarding the impeachment trial is that "impeachment" occurred in the House while Trump was still president and the trial is a separate thing to either convict or acquit, thus he is already impeached (while in office) and the Senate rules whether there should be further punishment than the "impeached" label. Conviction would result in removal (if still in office) and nowhere does there seem to be cover to forbid from running for president again, so this is where the real gray area is in my opinion. Furthermore, Trump being a private citizen at the time of trial is what seems to give the cover that the SC Chief Justice does not HAVE to preside because he is no longer the president.

If you read the Constitution article regarding impeachment you will see that it is written ambiguous enough to cover this line of thinking, which is what I bet the Dems are planning to fall back on if, in a normal law abiding world, they would be questioned / held responsible for their circus. CNN and their ilk are just running with this gambit to push the "Trump bad" nonsense to trick the masses, then it will disappear as quickly as it appeared after Trump is acquitted.