Two teams did this for Price with Drew Smyly and Norris.
Both of those pitchers are significantly worse than Price. Both teams got worse pitchers for more years of control. If you want to trade Jake for some future MOR, sub 2 WAR pitcher, I don't really see how that trade helps you either win in 2017 nor do I see how that trade helps you in the future.
And Detroit trade Smyly knowing they could "flip" Price if they weren't real contenders. And look at Smyly now: he's not even a full-time starter.
The Cubs can't trade Arrieta, a guy who has even less of a track record than Price, and expect to get back either a pitcher who is as good as him now nor can they expect to get back a guy who projects to be a 3-4 WAR pitcher in the near future. They can probably get back a Smyly or Norris but both of those guys are not TOR arms so I fail to see the value in that for the Cubs. The Cubs don't have a lack of quantity in terms of pitching prospects. At the very least, they can probably roll out three guys who get you at least 2 fWAR in 2018 and beyond in Hendricks, Lester, and Montgomery. What they lack is a guy who can replace Arrieta as a potential power arm who can win close to 20 games and be a 4+ WAR pitcher.
If the Cubs did something like Arrieta + Soler + Underwood for Paulino in Houston, that's something that intrigues me. But I'm not sure even that's enough to get one arm in Paulino. But that's the kind of deal you have to do with Jake: you have to attach younger guys to the deal and give the other team some sort of future value to the deal. Because Arrieta at this point isn't a strong enough pitcher/asset by himself to get teams to give you the quality arm that you want.
But I don't see this "the Cubs can't give Arrieta a long term deal" that everyone says. The Cubs gave Lester a six year deal through his age 36 season but while Jake is older, he has significantly less professional innings. Jake is at 1500 career innings while Lester was essentially 1800 professional innings between minors/pros/playoffs.