If a projected top pick says they won't sign with any team except their preferred teams, it still doesn't mean teams won't draft them.
A team could easily draft them and tell other teams the costs are 3 or 4 first round picks or they will simply hold on to them all season.
If the player does not sign their contract, they can re-enter the draft the following year though they will have lost a year of stats, salary, etc. and they may be in less demand the following year.
That said, the same thing could happen to them the next season as well.
The Archie and Eli Manning situation worked out for them because they found a team with a close pick willing to trade and capable of getting their plan B player.
If Shadeur said he would only play for the Cowboys, then 11 other teams would be incentivised to draft Shadeur to extort a lot of draft picks in return from the Cowboys, who have a history as we all know of overpaying in draft picks.
Not to mention, it creates a problem for Shadeur because his predeterminined rookie contract is based on where he is drafted. That would mean a team would have to draft him and then trade him to the Cowboys or else it would end up costing him a lot of money.