The thing that makes this costume the most interesting is what it would have said about the character of Hawkeye that could have been potentially different than the version we got in the Avengers.
While it’s never specifically stated where Hawkeye’s costume comes from one just sort of assumes it was S.H.I.E.L.D. issued.
If S.H.I.E.L.D. is just cool with Hawkeye pulling whatever out of his closet, it potentially means the man and the organization could have had a somewhat different relationship.
He’s a S.H.I.E.L.D. agent when we first meet him in Thor and whether they provide the uniform or he has it made, the formalness of it shows his connection to the organization.