Nancy Pelosi proclaimed that impeachment was forever. The approach that you suggest will ensure that her slogan will be the one that lingers. Only a verdict will deliver a better prononcement: Vindication is forever. Dismissal is what you have to do when you don’t have the votes to declare not guilty.
Just the opposite.
"Impeachment" means an adjudicated charge, in this case a CHARGE of Treason, Bribery, or other high Crimes and Misdemeanors. The impeachment process is akin to a grand jury process - both amalgamate CHARGES. The Senate tries the one charged. The Senate does NOT REMOVE the charges, only decides whether the target is guilty or innocent of those charges. The impeachment, as with Bill Clinton's, remains.
Your approach RATIFIES the House Impeachment process and charge, regardless of Senate results, which is what Pelosi was talking about. The Senate can rule Trump innocent but the impeachment (charge) is not erased.
My argument is the House impeachment process was unconstitutional, illegal, and thus, invalid. My argument is the impeachment itself should be thrown out for the reason I previously gave.