Objects in higher orbits are slower[1] than objects at lower altitudes, and debris from a hypothetical collision between two high-orbiting objects would not accelerate to a speed "far greater" than the originating objects, because that increase in speed would require some form of acceleration. One satellite smashing into another would not add sufficient energy to the debris to alter its speed significantly. Any change to the speed of the resulting debris, if it were to occur, would also necessarily alter its orbit. The object's speed and its orbital altitude depend on each other.
> So failure at very low orbit might add a lot of debris to higher orbits that might trigger Kessler syndrome.
It should be noted that "failure" does not mean "exploding into a thousand pieces", so a malfunctioning satellite by itself is not that much of a problem. Low altitude satellites such as Starlink are actually better from a space junk perspective — their altitude means the effect of atmospheric drag on the spacecraft will eventually (within months, sometimes) cause it to re-enter the atmosphere instead of just hanging around in Earth orbit forever, like dead satellites do at higher orbits.
Kessler syndrome would be more likely to occur with satellites in medium and high Earth orbit, since there is no drag to bring the dead spacecraft or debris back down to Earth. Anti-satellite weapons are particularly dangerous here, because they're likely to target high-orbiting satellites and leave debris fields behind.
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[1] As pointed below, in terms of pure kinetic energy this is not correct. I was referring to apparent speed vs an object in low-Earth orbit.