We absolutely need measurements. to confirm the design, specs, correct performance to the design, etc. we need to confirm the design meets design intent and we need a base line.
The real question is are we measuring all the right things? Can we even measure the things our brain/ears hear? how do we deal with bias? how do we deal with each persons different hearing/brain interface?
Its not a simple yes or no question like so many would like to think. We need measurements but we need to listen as well. We are not measuring or not able to measure everything we perceive in sound. Yet!