Elon Musk trying to save humanity from going extinct as a "one planet species" and in the process causing us to miss a near-Earth asteroid whose impact wipes us out would be rather ironic.
The ironic thing would be if we detected a large asteroid and had no way of deflecting it in time because we had shutdown SpaceX in an attempt to better find smaller asteroids.
The lower the orbit, the more quickly objects de-orbit. This is especially true of the lowest LEO orbits that Starlink sits in, where atmospheric drag also enters the picture. Worst case scenario, a totally dead satellite will deorbit on its own in a couple of years and they can very easily suicide if required to avoid catastrophe.
I'm not a rocket scientist, but this seems unlikely; sure two large satellites colliding could create smaller debris with a much higher apogee, but it seems to me that the perigee would not increase, so it would still spend a significant fraction of its orbit in atmospheric drag.
Kessler syndrome will never prevent us from launching things, it could theoretically stop us from parking things in certain orbits, but the risk to launch through those orbits will be minimal.
We've already detected all asteroids with that mass in our solar system [1]. There are smaller ones that won't end life on Earth that are still concerning, but the quandary is we have almost nothing to do even if we detected a threat from an asteroid.
Only in the near planetary region of the solar system. There's lots of comets with very long periods we didn't detect yet, because their last visit to the inner solar system was centuries or even millennia ago.