There are 2 perspectives from which to look at this?
1. Would (should) the Steelers trade him away?
2. Would (should) the Cardinals trade for him?
I mulled over perspective #1 and came up with the following:
If you were the Rooneys and you were mapping out the destiny of the Steelers 1, 3 & 5 years out, what would life be like in Pittsburgh with Roethlisburger still the starting QB?
A case could be made that he'd wind up being the centerpiece in a "soap opera" distraction that would be a millstone around the neck of the franchise. The Rooney's might simply decide that it's time to make a clean break right now and then move on.
From the Cardinals' standpoint, setting the personal-issues aside for a moment, it would come down to how much they'd have to give up in order to bring in a young QB capable of taking them to the Super Bowl each year. (I'm guessing that the price would be too expensive - we'd have to sacrifice too much at other positions or in draft picks to make the deal worthwhile).
Then add in the personal-issues and other risk factors - there's the "character issue", the marketing issue (of alienating fans), the suspension issue (one more misstep and poof!), the future behavior issue (can you really ever change behavior in an adult)? and the "we know him/you don't/he's really an OK guy" issue.
All told (admittedly without knowing all the ins and outs), I'd think the ratiio of risks + costs vs. benefits ratio would be too steep.