Yes, everyone needs to be fast. LB's should be 50-60 speed by seasoned, and 70-75 speed by Vet. Otherwise they'll typically have HB's run around them very often and you'll have trouble when you blitz with more than 1 LB, assuming you have one dedicated blitzing LB with 95+ speed. And even DE's should be 40 speed at least, preferably more. There's nothing worse than having a DE break the block and just be unable to run the HB down behind the LOS, or having a bunch of Hurries that were tantalizingly close to being sacks.
It's an extreme liability to have any defensive player under 40 speed at seasoned, who isn't on the D-line, and at Vet, everyone should be at least 70 speed except D-line. Yes, ballcarriers run slightly slower than a player with no ball in their hands, but it's still very important to have enough speed and pursuit to chase down the outside run, especially with the current meta right now.