I'm a huge LSU fan (my brother is there and I was at LSU-UGA this year), but #1 overall is too high for Devin White. I'm skepical of the transformative power of an ILB in general, and I think that last year, even with bad coaching and a terrible offense, this defense was league average.
The problem is not the defense or the defensive personnel, it's a historically execrable offense. I think that you have to take a risk on a foundational defensive talent for the next generation (who would come into his own just as Patrick Peterson begins to decline), or you try and transform the offense if you feel like you have a transcendent opportunity.
Among the opportunities in a trade down, I don't mind getting Devin White if someone like Ed Oliver, Jonah Williams, or Clenin Ferrel are already off the board.