Yaakov Avinu and Moshe Rabbeinu didn't wear hats and jackets, either...
Of course they didnt. That could have led to machlokes, with future doros being medayek exactly what they wore: bent up or bent down hat, borsalino, brandalino, stetson or roche, black, grey or navy, wide or narrow brim, high or low ribbon, with or without the brand name on the bow, gekneitched, sameter, beaver, turban, fez, beret, sombrero, bowler hat, perhaps Moshe wore a bush hat?
As to their suits, was it a langer rekel, a frak, with buttons on the back or not, a beketcher, a saville row suit, right over left, left over right, a robe etc. etc.
So instead they left us in no doubt at all as to their true affiliation, and as my kids school picture precisely and accurately showed a couple of years ago, Moshe Rabbeinu proudly and decisively led us out of Mitzraim... wearing a Streimel!!