I have not seen great reporting on the cap implications of an Aaron Rodgers deal. It would be absolutely massive for the acquiring team. They have tricks to spread it out over multiple years, but it's still a huge number.
As I understand it, a trade would accelerate about $40 million on to the Packers' cap. If they waited until after June 1 to do the trade, they would push off some of that money to 2024. I don't know their current cap situation, but I assume that taking on a large accelerated hit would require them to clear space.
As for the acquiring team, they immediately take on a $60 million cap hit for 2023. They could choose to apportion that over 4 years, at $15 million per year. But, $60 million is $60 million. As a practical matter, though, they are really taking him on for 2024 as well, at another $47 million. They have to decide before the 2024 season, and I think his contract for 2024 becomes guaranteed quickly. The reason I say that as a practical matter they have to keep him on, it's because if they don't, they basically accelerate the $40+ million that they spread out over 4 years. If Rodgers were to retire, though, they get out of the $47 million. But he will never retire when he could earn another $47 million for one more season of work, I wouldn't think.
So, the bottom line is that an acquiring team takes on a $107 million cap hit for two years of Aaron Rodgers. They could manage it to spread it over a few years, but $107 million is $107 million and so you're mortgaging your future. I can't imagine taking on a cap hit of over $50 million per year for a QB and giving up two first round draft picks.