Indeed it is important and necessary that those in office do not overstep their constitutional authority. There is no authority given the President of the Senate to override the will of the Senate or Congress as a whole.If the exiting Vice President gets to override the states and pick the next President, you would never see another Republican
What Patriots were asking for that day was not unreasonable. They didn't want Pence to override the election or pick the next President. They just wanted him to delay the certification until investigations into election irregularities were completed. But Pence knew, as they did not, that he had no authority and shouldn't have authority to do that for the same reason SCOTUS stopped the stupid 'hanging chads' recount in 2000.
Had SCOTUS not stopped that recount and certification of that vote been delayed, it also would have set a horrible precedent for all future elections as well as handicap the incoming President who needed to set up his staff and cabinet and be ready to govern on Day 1.