May I suggest this is impractical
It's impractical for the same basic reason that you can't trust a freeway full of cars to guarantee a 50-car pile up during every rush hour.
Yes, there are certainly more than enough cars on the freeway to fall into the Kessler Syndrome kind of statistic.
True, many cars (but only many) are driven by competent drivers who can be trusted to react in a reasonable manner to the growing chaos.
True, unlike space, freeways only move in one direction (not three).
But the problem persists — and yet almost never happens.
The Kessler Syndrome is a statistical analysis. There never has been and never will be a guarantee of any catastrophe. You could lob Buicks into LEO hourly for a century and, despite cluttering up LEO something awful, all you have is a statistical chance of a cascade failure that may never happen. In fact, let's look at a terrestrial cascade failure.
Let's consider forest fires
Forest fires are the real-life epitome of the Kessler Syndrome. Too many trees in close proximity that get older and dryer with every passing year just waiting for that one random lightning bolt1 to start the cascade failure. You betcha! Forest fires happen every year! But when was the last time you saw the entire forest burn down? It almost never happens. In fact, keeping everything out of LEO via Kessler Syndrome is like expecting the entirety of Canada to burn to the ground in one huge forest fire. It could statistically happen — but it doesn't. Why?
Mother Nature stops them by hosting areas without fuel. Like deserts and lakes.
Humanity stops them by creating unnatural areas without fuel, like large, paved roads and fire breaks.
Both humanity and Mother Nature can stop forest fires by dowsing everything with water (or some synthetic equivalent).
How does this relate to space? In the immortal words of Douglas Adams, "Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space." There's a lot of dead, "fueless" space out there. Yes, the statistics say there's a growing problem, but that's just statistics.
In reality, there's a whole lot of nothing where debris can harmlessly exist.
Large satellites must be hit by high-energy objects or they're more likely to rob the process of energy than they are add to it. That's one of the reasons freeway pile-ups come to a stop. With each collision there's less energy to cause the next collision (and more time for motorists to realize what's going on).
And that last bit is important, just like flying planes full of water and motorists realizing something in front of them is more important than the text they're trying to write, satellites with modern tech have the ability to move out of the way. Older satellites have less of this ability. No, it's not perfect — but neither are airplanes full of water or attentive motorists.
And yet there aren't daily 50-car pile-ups on congested freeways.
Are my metaphors perfect? Absolutely not! But they make a point. The effort you would need to put into causing and sustaining the Kessler Syndrome is so much greater than the benefit that it isn't worth pursuing.
It would be cheaper to fire missiles at every launch than it would be to trust in and maintain the Kessler Syndrome.
Keep in mind, Kessler proposed his problem in 1978 — and despite an increase in satellite launches, it hasn't happened yet.
Yeah, but I really, really, really want to use the Kessler Syndrome to keep satellites out of orbit! What can I do?
Use the modern equivalent of a flak cannon. Your Evil Overlord sends up a constant flow of disposable satellites with hundreds or (preferably) thousands of #10 cans full of 1" ball bearings, C4, and a timer. The cans are sent out spherically from the satellite for maximum spread. Like deadly fireworks, they'd send their cargo of ball bearings (quite literally quadrillions of them) into space! They'd cause havoc for as long as you keep sending up satellites — and with each destroyed satellite, you add to the mahem!2
1 Or, in the case of your Evil Overlord, that one deliberate match thrown by a stupid teenager who thinks the result would be really funny.
2 And to top it all off, if you're really lucky, you'd have a constant light show in the sky as bazzillions of 1" ball bearings burn up in the atmosphere. Glitter! So much glitter!