Yes, but they will likely be significantly influenced by room interaction, but for example, crosstalk is as a good an indicator of soundstaging capability for an amp.Exactly.
Soundstage width, soundstage depth, instrument separation are all important factors to how a system sounds to me.
Are there measurements to show these traits ?
Consider the industrial applications say for a signal amplifier, if you were installing into an aircraft, there is a clear process of certification to prove that the component works. This is achieved by characterising it by objective measurement, not be a subjective assessment. Testing electronic components is not new, nor difficult; it's just not in the commercial interests of consumer electronics to do that, so a bit of smoke and mirrors helps drive those margins.
The really difficult part of consumer audio is to try to quantify the psychosomatic effects, blind ABx testing goes someway, and the development of some form of average standard sound from Dr Sean Olives work for Harman Audio tries to address the natural variation of the human form and corresponding aural response to the same stimuli. In all likelihood, present 100 people with a a selection of tailored profiles and they won't agree which sounds the "best"
Good specs mean that the kit does the job it is designed to do, but it doesn't mean that you personally will like that sound in your room.; however, as I said before using that data as a starting or reference point can more quickly get you to where you want to be, rather than watching youtube or reading subjective only product reviews. I can't stress the influence of room response though, it is way more significant than what amp or dac you use, so if you're going to measure anything, I'd start there.