This might actually lead to a greatly increased risk of creating an impenetrable field of space junk if the thousands more satellites that SpaceX launches collide in to one another.
If that happens expect SpaceX supporters to start singing a different tune.
How often? You'd need a pretty lucky collision to knock something into a higher stable circular orbit.
Here is an article in Nature [0] discussing other risks, and mentioning that LEO is already in the early stages of Kessler Syndrome, while SpaceX alone is seeking to launch as many extra satellites as there are tracked pieces of debris already in orbit, with several other companies having similar plans. They also mention that debris in one orbit can cross to other orbits.
You seem to be referring to the Kessler syndrom. If that happened, it would not mean that we could not send probes to space anymore. It only becomes unviable to have satellites at the altitude of the debris field. We could still launch through it into higher orbits or onto interplanetary trajectories.