Should a reference speaker be neutral, or just great sounding?

This is a great question.  From a purely philosophic perspective, I would agree that you would want a speaker that has a perfectly flat frequency response from 20hz to 20khz and compare deviations in terms of sound profile.  If everyone had this as a baseline and new what this sounded like, reviews would be exponentially more valuable.  

However, even if you found this speaker, it would most likely not behave that way in your room.  Your choice in amplification and source is going to alter its sound profile.  And finally, it may not be to your liking.  Just because something is conceptually ideal, doesn't mean it is your preference.  Additionally, wouldn't use a speaker of that sort to evaluate a 300B SET.  

Philosophically, I get it.  In practice, it might be better to choose a speaker in every BestBuy as your "reference" so that people have a common, mainstream point of comparison.  

I fully agree with audioquest4life response from above. Also, consider what speaker was used in the recording studio(s), especially in the past. I've seen most all studios use Yamaha NS-10 speakers to monitor the mix. IMHO those speakers do not sound great but they translate well. Meaning what you hear on those will closely resemble what you hear on a tabletop radio, home stereo... Those are used for near field monitoring. As for main monitoring in a studio, in the 70's JBL was a mainstay like the 4311's or 4412's. Going further back for main monitors the Altec 9844a was a standard. Today I see lots of big studios using custom made main monitors based on the design of the 9844a. Also, today for near field monitoring I see Genelec speakers most often.

“Should a reference speaker be neutral..”

At first glance, I get what the OP was asking. But upon deeper scrutiny, the exercise seems a bit ludicrous. And at some level, it’s like finding a solution to a problem when a problem doesn’t exist.

- The OP is asking for “objective” factors from “subjective” judgements- this doesn’t exist. While some would say linear 20-20khz is a criteria, a tube guy may not care about linearity at all. Does that mean tube guys has no point of references? Of course not. Speakers are imperfect facsimiles of reality.
When evaluating speakers, people have different subjective importance/ranking of bass slam, midrange, transparency, clarity, musicality, detail, extension, etc. Trying to establish a one size fits all....

- Reference can be defined as any point in which other points compare. So technically any comparisons can be said to have a reference. We couldn’t survive without comparison of choices.

- Reference Speaker as defined by an audio reviewer as being the subjectively best speaker he has heard to date. This too has its limitations. Audio reviewers can demo only a small sample of what is available. As such, their “reference speaker” is limited to this small sample. Ever notice that reviewer reference speakers are rarely the same amongst reviewers? If I were to demo $5k speakers to come up with a favorite aka reference, while another demos $100k speakers to come up with his reference, Seems obvious that these two references aren’t really the same.

- For personal audio, what value is having a reference speaker (as defined as an audio reviewer) in the first place? Unless you’re trying to communicate to others like audio reviewers, isn’t our personal speakers simply evaluated by personal preferences? Don’t we subjectively simply say speaker A has this these positive/negative traits, and speaker B has these positive/negative traits...? Seems unlikely that we’d elevate a single pair of speakers to which all others will be compare to.