Actually I would prefer the Packers to hold on to Jones if he makes it clear that he doesn't show up for minicamp. Collect the fine and send a message to other players that they can't force the team's hand by not showing up.
Anybody who wants out this badly because he does not like his diminished role should be accomodated. Taking the approach you and others have suggested says, in affect, other guys who want out just as badly should keep it to themselves. I'd want to know who they are and would try to accomodate them. A guy in a similar situation would be Fackrell, with Smith, Smith and Gary jumping ahead of him on the depth chart. If Jones was traded or cut fine-free, thereby emboldening Fackrell to a "me too" moment, I'd oblige him as well.
Now, we can't expect anybody to be "Packers, do or die". It's a business, so goes the cliche. I'm sure there are a lot of guys on the roster who are playing for that second contract, wherever it might land them, which is what this is about, Jones wanting to be where he can get those needed snaps. But if a guy publicly demands to be traded and then doesn't show up, he has made clear he doesn't want to "do his job". You don't want those guys around. Letting them be around so you can fine them and then cut them is, as I said earlier, simply spite and a deterrent that smells like fear: "If that's the way you feel, don't embarrass me. I don't want to know about it." That's no way to run a railroad.
It's really a no win situation created by Jones. I'd take the high ground which is "team first, do your job".
We've heard a lot about accountability in the last couple of years. I think it started with the Randall incident. His tantrum was a public affront to the coaches and "do your job". It probably wasn't his first incident that could be attributed to a "crime of passion" in the heat of the battle. The players leadership council, by whatever name they give it, recommended Randall be traded. McCarthy and Thompson opted for damage control because of lack of options on the roster, whatever trouble he might cause or failure to do his job is better than the next man up. That was a mistake.
Gutekunst didn't waste much time in trading Randall. He didn't bother waiting around for the draft to see if he could land a replacement. That would have been lame. As soon an Clinton-Dix did his "I don't think I'm not going to be here next year" routine, a public expression that he was not happy playing without an extention, he got traded faster than his head could spin.
If what we want is accountability and not trying to bury discontent through some kind of deterrent threat, then Gutekunst should trade him or cut bait at the earliest opportunity.