You use the exclusive tag so nobody can sign him to an offer sheet.
If they signed him to a non-exclusive, somebody could sign him to an offer sheet and Dallas could either match or let him walk and get 2 first round picks. Problem is that you dont know if the team will poison pill the offer sheet to keep you from matching.
For example, say a team that has a really good defense but no legit QB, like the Bears...…….decide to give Dak an offer sheet that says if he plays more than 3 games in the state of Texas, he gets a $200 million dollar bonus in addition to his contract. Obviously, Dallas could not match that and would have to take the first round picks, which would probably be low first round picks since the Bears are a pretty good team.
That is why you use the exclusive tag, it prevents teams from doing something just like this. While poison pills are discouraged by the league, the owners never passed a law forbidding it. So yeah, its a total dick move to do it, but its still allowed.