The problem is you need to destroy more debris than you create with your shield.
https://www.technobyte.org/wp-content/uploads/2017/05/How-do...
1/2 oz piece of plastic into Al at 15k mph: https://external-preview.redd.it/oi0C_a113_sSzHtSaPvzn6_0Gfg...
The thing is at orbital speeds colisions are VERY energetic events that don't behave likey normal low speed collisions. The thing coliding effectively turn into rapidly expanding plasma before any of the expected plastic deformation, shearing, etc. one would expect on a low speed collision (say a truck in full speed hotting a wall).
When you think about it, this effectively all the fuel and oxydizer that has been used to place the given object into orbit releasing all it's energy at once in a very small area.
As an example let's say your steel plate manged to hit a 700 kg satellite at ~8 km/s, which is perfectly possible with, with the worst case being a 16 km/s combined in a head on collision. How much energy will get released ?
Say the sattelite has been put in orbit using thr Soyuz 2 launcher, which can accelerate up to 7000 kg to tje orbital speed of 8 km/s. Soyuz 2 weighs about 312 tons, more than 90% of which is fuel and oxydizer. It could launch 10 of our 700 kg satellites.
This effectively means a 700 ks sattelite hittimg your 8 ton steel plate is equivalent of a point detonation of ~30 tons of perfect mixture of liquid oxygen and kerosene.
I don't tging a 8 ton steel plate will survive that in any usable shape.
It's only unsolvable in the current context that a nuclear bomb going off in MEO or GEO is worse than some space trash. If the situation became dire enough that we couldn't get off the planet, then you could just detonate some high yield explosives in orbit.
https://en.wikipedia.org/wiki/High-altitude_nuclear_explosio...
Though dead satellites in GEO make a lot more news.