A lot wrong here.
No team is going to "over offer" to box the Cowboys in, but they'll do it because they don't have a quarterback. That's how free agency works at every position, in every sport. There is no chance Dak gets offers at less than "market." Crazy to think that.
It doesn't matter if they sign the tag or not. The Cowboys control if he accrues a season by using the tag. If Dak chooses to sit out - which would be beyond stupid - the Cowboys can just place the tag on him next year again. By opening the door for other teams, you're losing control of the price. Dallas, with the tag, sets the price at $38, and that's where negotiations start. Same thing they did last year at $31. When you go non-exclusive, you let some team - say San Fran or NE - offer $45 and Dallas now has no negotiating control. You're delusional if you think a team wouldn't do that.
There is just absolutely 0 upside to the non-exclusive. It results in having a more expensive quarterback or no quarterback.