> That could literally produce no output program?

Way worse than even that (you might be noticing a theme here...). Once the optimizer has removed as dead code any branch that, if taken, would provably lead to UB at some arbitrary future point of execution, it can conclude that the other branch is now the only possible execution, and call it unconditionally, even if that leads to removing all your files (the classic example is https://kristerw.blogspot.com/2017/09/why-undefined-behavior...).

Yep! Dumb example.

    main()
      x = get_from_some_external_data_source()
      if x:
        print("Hello World")
        trigger_ub()

You might expect this code to always print if x is true but the optimizer can look at this and say "welp, if x is true then it would trigger ub, therefore it must be false, and since x must always be false we can just remove that entire branch."

c.f. “nasal demons”