Getting some of my track athletes ready for indoor season we do a lot of different stuff with sled dragging.
One of the things that we do is timed pulls for a specified distance with varying amounts of weight. Always walking, never running, but they are to walk as fast as they possibly can.
What we discovered is that as we added more weight, the athletes began to pull the sled faster and faster, which makes sense because they were able to push harder against the sled.
Obviously there is a point of diminishing returns on something like this but the principle really applies to speed training in the squat or bench press.
Training your body to produce more force requires you train with the right weight as well as quickly. This is also where accomodating resistance comes into play. If used correctly you'll actually end up being able to move weights faster.