The something we will get from him is depth on the offensive line, in case of injury, during a season the Cardinals will be in the mix for a championship. Even if his production for this year is only a single game that helps bring a trophy, that is more valuable than a future mid-round draft pick.
For Massie, it would be better to show a commitment to his current team and give the appearance of taking the suspension and possible demotion like a man. Free agency can bring a sense of desperation for some organizations, and if more than one team is interested, Massie will get a nice pay check. Pushing for a trade, and spending half the season trying to adjust to a new team (either on the bench or looking bad) could easily diminish his value - not just in dollars but in the number of teams looking to bring him in.
Even if he just rides the bench, it is worth it to the Cardinals to have someone on the roster ready to step in. During the off season, Massie's agent can easily spin the 'got in the doghouse, but has learned from it' angle. It is just too risky (for both sides) to trade for a mid-round pick. Not to mention the risk of the other franchise handing over a draft pick for a possible non-starter, already with a suspension, that is in his last contract year.
Just don't see the value for any of the involved.