There's a financial benefit to waiting until after June 1, but beyond that there's zero reason why they wouldn't want 2022 draft picks. Unless you're wanting 22 to be a 'tank' year, which I suppose is possible though unlikely. Beyond that dates are fluid prior to the start of the league year. Rodgers has said he'll make his choice known prior to the end of the March 8th tag deadline, so there's that. But, I'd expect all parties involved (Packers, acquiring team, Rodgers) would want that known as far in advance as possible.