Is it possible to have an accurate speaker

I think the point of any good speaker is to reproduce whatever is put into it. If it always sounds "round" or "warm" regardless of the source it can't be particularly accurate as, after all, music tonality is nearly infinitely variable. Or something.

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.

If you know what the hell you're doing (and aren't deaf) ANY system can sound fine usually. Bands with too much stage volume are hardest in small rooms, but otherwise I find that keeping the hell out of the way with good mics, no compression, understanding trim pots, and having plenty of power amp headroom does ths job.