A problem, but not an insurmountable one.

Being hit isn’t the same as being destroyed, you can track and avoid large objects, and small are survivable in the short term. https://en.wikipedia.org/wiki/Whipple_shield Collisions however keep adding up until a satellite fails.

Second an outbound rocket need not be in orbit, so if it is destroyed that may not result in extra orbital debris the overwhelming majority of mass could fall back to earth.

Also, Kessler syndrome isn’t a forever thing. There’s a reason planets have rings not debris clouds. It’s possible to have a steady state where the rate you’re making it worse is balanced with the rate things are naturally clearing.