Although I believe speed to be under-rated globally, there are exceptions to the rule of 'more speed better'.
Sometimes more effort has such minimal returns that speed increases are not worth it. More effort will only burn you out. See Derek Sivers' story of the bike ride for a great example of this:
So apparently all of that exhausting, red-faced, full-on push-push-push I had been doing had given me only a 4 percent boost. I could just take it easy and get 96 percent of the results.
Some improvements require period of integration or recovery that cannot be accelerated. For example, lifting weights 10x a week does not necessarily increase your strength more than training 3x a week; your body needs to recover. Likewise, skill development may need periods of reflection before advice can be internalised and acted upon.
Speed is useless if you're going in the wrong direction. Aim for the vector, velocity, not speed. Focusing on speed can crowd out your direction finding ability and encourage you to head in the wrong direction.
Tortoise and hare dynamics may come into play: sometimes slow and steady wins the race. A dragster may win on a quarter-mile, but if you're racing across tough terrain, a bicycle might be quicker.
See also: Speed matters more than you think