Just because we may not be able to concretely define what makes art "good", does not mean we can not discuss why we like it.
If one person enjoys a piece because they appreciate the technical mastery of the brushwork, another enjoys it for how accurately it mimics reality, and another finds it special for the feelings evoked by the composition, each of those people can articulate why the piece speaks to them. They can describe why they like it, there's no reason anyone should suffer any sort of explanatory atrophy.
Now, can any of them convince another that the work is better than another? Probably not. The person who enjoyed the brushwork may find an even more masterfully painted piece, which they think is better. But perhaps the new piece doesn't demonstrate quite so much clarity in portraying reality, so the person who enjoyed that from the first piece still prefers the first. Who is to say whose values are more important?
For this reason, I think the multi-axis view is more constructive. Rather than spending our time arguing if technique or novelty or emotions or whatever else are what matters most, we can focus on appreciating each aspect as we see fit. And we can certainly articulate what a piece does well on any axis.