And this isn't theoretical. I've seen ignored errors do damage in the past. Was infuriating to see that we had set a top-level exception handler in our server that just logged and kept going. We had a couple tables in our database trashed because of that and ended up having to restore from the nightly backup, losing everything that was changed that day.
What do you you think the default behavior of an assert is? If you are turning them off, then you get what you describe, which is not what I am advocating.