I don't think we're going to accept "pair" as the plural of "pair". If we did, it would also be accepted in the other direction (English for German speakers). I wouldn't be comfortable with that.
"In informal North American English some people use pair as a plural form: three pair of shoes. This is not considered correct in written English."
Similary with other measurements or quantities:
- drei Liter Wasser / three litres of water
- ein Pfund Mehl / a pound of flour
- ein Glas Milch / a glass of milk
- zwei Stück Schokolade / two pieces of chocolate
English likes to add "of" in measurements, German doesn't need it. (And it often uses the singular for quantities as well.)