Don't assume a greatsword for a fighter because all races can't use that. You say you want to eliminate race as a variable, yet you assume a weapon not able to be effectively used by all races, and worse a weapon that some races can't even get a feat or multiclass to be able to use.Your argument is a poor one and ignores common sense and the scientific method.
When you balance and compare things you have to control variables. Race is a variable and to control it, you take a vanilla human with +1 to all stats and use it for every class. That way everyone can get 16 in their main stat. Then you balance all classes around that.
Some races will make classes better, some will make some classes worse. But, all classes should be balanced outside of the race.
It is great not to want a variable because of race, but that is a poor choice when you choose as your standard one of the most uncommon chosen races. Standard Human is a poor race to use as a basis for comparison as virtually no one plays that race. You should choose variant human, which is the most common race, and a variant human Monk can use a longsword at level 1.
Bottom line, either you are allowing racial traits or you are not. You can't have it both ways, and if you allow some of them, you need to allow all of them. Otherwise you are just picking and choosing which ones to allow to strengthen your argument.