If the Vice President has the authority you say, what prevents Harris from tossing the electoral vote in all the states Trump wins? If there's a Democrat-controlled legislature in that state, they can swap the vote and declare Biden the winner.

That's why the VP wasn't intended to have that authority.

When there are disputes in a legislative body, it usually is resolved by voting. If Congress has no role in the vote count, then it would say "The VP counts the votes by himself in his office and then announces the winner."