General manager Steve Keim understands the dilemma, but noted during an appearance on 98.7 Arizona's Sports Station that there isn't a simple solution on setting a timeline for when the Cardinals will turn to the rookie.
"It's a tough question," Keim said, via the Cardinals' official website. "When the time is right, Josh will have his opportunity.
"At the same time, you never know how a guy is going to be affected. Some guys have played too early and it has crippled their career. I'm not going to name names, but I think a lot of us can think of certain players. Then there are guys who have come in and had success right away. But usually it's a rocky road."
Keim raises a valid point, of course, as the league is littered with high-profile quarterbacks who've seen their careers grow stale. Most recent examples include former New York Jets second-round pick Geno Smith, who tossed 21 interceptions during his rookie campaign and is now a backup with the Los Angeles Chargers, and former Jacksonville Jaguars first-round pick Blaine Gabbert, who is on his fourth team since entering the league in 2011.
"I don't think there is any exact science to that," Keim said. "But I think there is certainly a feeling of knowing when the time is right."
The key for the Cardinals going forward is determining when to turn Rosen, the 10th overall pick of the draft, loose on opponents even as the team struggles.
With Cleveland Browns quarterback Baker Mayfield winning in his professional debut against the Jets on Thursday, Sam Darnold opening the season as the starter in New York and Buffalo Bills rookie Josh Allen seeing action, Rosen is the only quarterback selected within the first 10 picks to not play yet.