They should each be interpreted in the context they're intended. What does it mean to describe a particular pain to be a 6 on a scale of 1 to 10? Or the numerical values on the Likert scale to measure opinion? Do these similarly blur the line between science and bullshit? The question "are we closer or further from global catastrophe?" is one worth trying to answer. The Doomsday Clock is one way to make this comparison. Indeed, the Doomsday Clock value is much more like pain or Likert scales in that it's used for comparison, as opposed to an absolute value.

I'm not sure what you're arguing so strongly against. I'm not saying the Doomsday Clock is perfect. I think it's useful. It can likely be improved. When/if we can find better quantitative representation for this, I agree we should use it.