I’m guessing they didn’t want to lose the Dallas market (and beyond) to the AFL Dallas Texans.
Exactly. Especially given that the AFL also had another inaugural franchise, the Houston Oilers, in Texas. Tom Landry, Offensive Coach for the New York Giants, a Texas native, who lived in Houston during the off season, had been approached to coach the Oilers.
In the then twelve team NFL, Landry was already considered a future head coach. Landry did not want his children growing up as New Yorkers, and coaching in Texas would allow him to be with them year round. The knowledge that Landry would certainly be coaching a professional football team in Texas, in 1960, added to the NFL's impetus to make the Dallas Cowboys happen.