Re: "Probably"?
Not really. You have very little to back up “we've cleared”. The big C one we all know about was 65M years ago which isn’t that old in a 4000M timeframe, so saying the cosmos has “shot its wad by now” doesn’t do it.
What we do know is that big C nearly wiped out all life on Terra. It’s a remote risk but truly existential. Even runaway global warming, much more likely, doesn’t reach that: oh, it may extinguish thousands of species and displace, if not kill, millions. But humans will still be there, with our trusty roaches and rats as companions.
A good deal of prevention dovetails nicely with better near-space exploration/imaging, which is worthwhile in itself. We don’t need to spend _that_ much money either: you’re basically putting up telescopes, tracking, cataloging and analyzing. A good chunk of that effort is computing which is cheap. Given enough lead time, even C could be deflected with our current tech (we’d “only” have to develop new engineering for it) and that will only improve. And even a city-killer would be nice to avoid.