The Hawks need another play maker to relieve and allow Young to play off the ball some. Murray obviously doesn't fit that bill and while White would, given the age gap between him and Avdija, Haliburton, Hayes (two of which should be available at six) they'd be better off selecting one of them.
Granted, there is some internal pressure to "take the next step", but even if they were willing, I doubt the Spurs would make that move.
Like they'd trade the third pick for an aging, pseudo star on an expiring (and given their situation, it'd take top dollar to get him to extend), when they have ample cap space anyway and Batum is expiring.