Should Speaker Manufactures provide a Frequency Response Graph?

They should at least make them available upon request. 

I have never been able to discern the voicing of a speaker from performance specs.

From manufacturer specs? That makes sense.
However, it is not difficult to do with thorough third-party measurements. It merely requires an understanding of how the measurements correlate to perceived sound quality. For example, take any two tweeters and provide a CSD/waterfall graph for each. Based on the graphs, I could tell you with certainty which one will sound cleaner and more refined.

Another example: a speaker with a wider horizontal dispersion over a large bandwidth will produce a bigger soundstage than one with a narrower dispersion over the same bandwidth.