The Constitution specifies that the Chief Justice of the Supreme Court presides over impeachment trials of the President. SCOTUSblog says that the reason for this exception is
In any impeachment case other than that of the president, the vice president can preside ... However, the Framers recognized that it would be unseemly at best for the person who would assume the presidency in the event of conviction by the Senate to preside over the president’s trial. To prevent that obvious conflict of interest, they specified the chief justice as a stand-in presiding officer in presidential impeachment trials.
The Chief Justice is not presiding over the upcoming trial of Donald Trump, because he's no longer the President, so that clause of the Constitution doesn't apply (another weird result of the unprecedented impeachment of an ex-President). Instead, Patrick Leahy, the President Pro Tempore, will preside.
I read in a news article that this is normal:
“The president pro tempore has historically presided over Senate impeachment trials of non-presidents,” Leahy said.
So if the VP doesn't normally preside over Senate impeachment trials, and the President Pro Tempore has no such conflict of interest, why was this provision necessary in the Constitution?
SCOTUSblog says the VP can preside, but in fact they don't. In absence of this provision, could the VP demand to preside instead of the President Pro Tempore? Or did the framers simply assume that the VP would normally preside due to their role as the President of the Senate, but tradition has changed this practice?