Why isn't there one exact measurement of earth's distance from the sun?

Answer 1

Because in the first place, Earth is never exactly "this" distance form the sun. It goes closer and further away during its orbit.

Secondly, the sun is not a consistently sized sphere. It bulges and crumps up and spits and wobbles; what was the surface yesterday might now be tens of kilometres deep, or hundreds of kilometres away from the surface into space.

Third, the methods used to determine the distance rely on slight errors in the tools used and the methodology; while several methods can give very close answers, they will never be perfect.