Is it possible to have an accurate speaker

It's just semantics but "warm" describes a particular type of sound. If everything sounds that way, it is probably not as "accurate" as it might be since these two words infer a different nature of the sound.

But its all semantics, ie meanings of words. Not of much value outside of discussion.

The only practical way to assess relative sound of different things is to compare them to a reference. ALways have a reference sound in mind for comparison based on systems and/or live music you have heard, if you care about these things. OR just listen to what you have and enjoy it for what it is if you can. Its all good. Technically right does not assure a happy listener. Music is art, though the gear needed to play it at home is based on science.

Well, if you want an easy answer you can take the many different, and opposing, opinions that you will surely get in response to your question (I like Mapman's, btw) and try to find some kind of concensus or distillation. Or, if you want a truly meaningful answer that will ring true no matter all the cries of: "you used different amps", "no two halls sound the same", "you don't know what the recording engineer had in mind", etc., you can make a commitment to listen to A LOT of live music over the course of, say, the next six months; and then you will have a better sense of what the ONLY true reference is all about. It won't tell you which speaker is accurate because there is no such thing; but, it will tell you which speakers get closer to being "accurate" than others. And some actually do a decent job of it; sometimes sounding "warm", other times sounding nasty and shrill and everything in between.

Without getting into details about diffraction loss or baffle step compensation, if you want them "warmer", move them closer to the wall.

The late Brian Cheney did some very impressive live vs amplified sound comparisons at a few hifi shows that must have been difficult to set up and the results were very impressive. Surprisingly, the general public didn't seem very interested in the most honest, no excuses, speaker demonstration.

As a professional musician I have heard some post production studios and even some sound reinforcement setups that were very well done. So depending on ones subjective criteria I would say yes there are some very accurate speakers who performance are very dependent on the room and the execution of their setup which, as a whole, is no small task.

In all, the one thing all this has taught me is that there is no such thing as a full range speaker unless it contains a separately and very robust amplified bass design.

As a (long, long time) professional musician and professional live sound tech I'm AMAZED at the ability of tin eared or otherwise incompetant live sound techs to make a good system sound bad, or they lack the skills to make a mediocre system sound good. My local well equipped concert venue (I name names...The Center for the Arts in Natick, MA, or "TCAN") recently managed to make Shelby Lynn sound like she was playing from inside a small can. She wasn't. This was one of many recent poor sounding shows there...at $45 per ticket (Lynn) the crowd deserves better.