@MissAnthrope I agree with the questions premise that the scoring in tennis is particularly arbitrary, more than in other popular sports.
In basketball, if a field goal was worth 1, how much would a free throw be worth? How much would a three-pointer be worth? If you changed a three-pointer to a two-pointer and a normal field goal to just be worth one point, long shots would become much more valuable, relatively speaking. This would significantly change the game dynamics, strategy, and required skill set. Two points for a field goal seems like the minimum whole number, without getting into fractional points.
Same in football. A touchdown is equal to two field goals, three safeties, or 6 PATs. If a touchdown was worth less, then you’d either have to get into fractional points or you’d change the game dynamics significantly.
I think the relative value of points in these games works quite well, as proved out my their huge popularity.
However, in tennis, the numbers seem unnecessarily inflated. Echoing @AstroChuck: Why shouldn’t it just go 0, 1, 2, 3, advantage, game?