It may be bad form (no pun intended) to start an article with a personal anecdote, but I'm going to do it anyways. I have added speed work into my programming multiple times over the years and never saw any benefit. This is not to say speed work is "bad", nor that it doesn't have its place in certain situations, but if you're training for a strength based sport such as powerlifting, maybe doing speed work isn't the best use of your time.
Force = Mass x Acceleration; you probably learned this formula in high school physics. The faster you accelerate an object (like a barbell), the more force you are applying. Technically speaking, acceleration is the rate in change of velocity (speed). If an object is already moving, like your car for example, and you press on the gas to go faster, a force is applied to increase your speed. The concept of speed work relies on this fact that the faster you can make the barbell move, the more force your body is generating. In theory, if we could make 225 pounds move fast enough, you could apply the same force as would be needed to move 315 pounds. Lighter weight means less stress on the body, but performing the reps as fast as possible means you should still getting some good work in. It's also thought that this directly translates to heavier weights, as the faster you can perform the lift, the better your chances are at completing it as less total time is spent under load. This seems to make sense, as taking 8 seconds to complete a grinder of a squat might feel more taxing then taking only 4 seconds to squat the same weight.
So who does more work, the guy squatting 500 pounds in 8 seconds, or the guy squatting 500 pounds in 4 seconds? The answer, which in my opinion is where the case for speed work starts to break down, is that they both did the same amount of work (before anyone starts arguing about body mechanics and limb length, let's pretend our squatters are identical twins). When gravity is constant, it always takes the same amount of energy to move an object a specific distance, regardless of how fast you move it. How quickly you can accelerate the weights doesn't really matter as much, because you are performing the lift over a distance. Giving the barbell lots of momentum in the beginning is great, but you still have to continue moving the weight over the entire range of motion. Our good friend gravity is always trying to pull the weights to the ground. Being able to generate lots of force over time is just as important in weight lifting as being able to generate a high initial force to get the bar moving.
My biggest complaint with speed work is that moving lighter weight faster does not prime your body to handle heavier weights. To get stronger, you have to increase the load eventually, there's no way around it. Being able to bench 225 really fast doesn't prepare you for what 405 feels like in your hands. Our muscles adapt to stress; as we get stronger we progressively add heavier weight in order to continue supplying adequate stimulus to force our body to respond. Does it make sense that moving a weight really fast would make you better at moving heavier weights? I don't really think so, you're just going to get really good at moving that weight quickly, which is really not the point in a sport like powerlifting. This isn't to say that I don't think practicing the movements as quickly as you can while still maintaining proper form is a good thing, in fact I always encourage it.
The other problem with speed work is that you're adding fatigue and spending training time on something that has minimal benefit. Each workout and exercise should serve a purpose. If you're looking to improve technique, speed work probably isn't your best bet as it's pretty difficult to maintain perfect form when you're focusing on moving each rep as fast as possible. Since you're using fairly light weight the carryover to strength gains also isn't going to be there. Similarly, if you're goal is hypertrophy, why not just add more volume into your normal working sets? Your muscles have a limit to the amount of work or volume they can recover from in a given period of time. Since more is not always better when it comes to weightlifting, wouldn't you want to choose exercises and loading schemes that give you the "best bang for your buck"?
I'd like to end with a disclaimer; I am not trying to demonize speed work. Do I think it will hurt anything if you add it into your routine? Not really. Do I think there's worse things you could do? Sure. Do I think it is an efficient use of your precious training time? Not at all. I can't say that I know anyone that's added significant weight to their lifts after incorporating speed work. I've personally never experienced any benefit. If you're still considering trying it, stop and ask yourself: "What am I trying to get out of this exercise?" Is it just to get faster? Why not put more emphasis on speed all the time? Try moving the bar faster while you're warming up. Prepare yourself mentally and stop overthinking the lift. Many times, our reps slow down when the weight gets heavy because we're hesitating mentally. What's another great way to get faster? Get stronger. The end.