There are special things to be learned when you consciously control and vary the speed of your grinding strength movements. Squatting feels a lot different when you do it for strict, timed intervals (3-count down, 3-count hold, etc.), and so does pressing, pulling and core work.
And it's worth your while for a few different reasons. First, moving slowly forces some of the same muscle activation required for smooth stabilization around a joint. The same "magic" that comes from giving someone the (appropriately) heavy weight as they learn a new movement can be found in slowing down those movements. Your body simply can't gloss over the phase of the movement that is weak as you might when you move quickly. This brings us to our second benefit: slowing things down in strict way demands that you work at a narrow range of intensity. While you can move a too-light weight slowly (and get lots of the same movement-learning benefits), you just can't control the tempo as the weights get heavy (for you)*. These kind of self-limiting bounds are the bread-and-butter of the bootcamp or small-group coach because they allow us to manage the highly variable and specific loading needs of multiple people in real time. If you can't move the weight with control, then you probably shouldn't be moving it at all!
Finally, tempo work provides a needed change of stimulus for your body. Improvement is only ever the result of recovering from new and greater demands, and varying tempo can provide exactly that sort of demand. Of course, returning back to your natural, undefined tempo can have the same effect, but now at a heavier weight. And so the quest for strength continues...
*and no, we're not talking about setting PRs here. Remember the part about doing most of your training at sub-max loads?!