Is it possible to have an accurate speaker

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.

Many underestimate the power and headroom needed for BEST not just good results.. One of the most basic and common snafus for all audio affectionados to address IMHO.

I went to a show last summer where I asked a vendor to play some Rush on their very nice high efficiency speakers being shown off playing small ensemble acoustic jazz quite nicely off a <10 watt flea powered SET amp. It was totally underwhelming and the vendor admitted that the amp was underpowered for the task. I could have been cruel and asked for some big band jazz, but.....

For most speakers out there, 80-120 SS watts might get you in the ballpark but more is needed usually to hit a homerun regularly.

Newer high quality high efficiency Class D amps are the ticket to get there without having to deal with huge, heavy, power sucking amps. That's progress! Take advantage of it!

No - it is not possible to have a 100%$ accurate speaker - nor is it desirable.

For example it is well known that the most accurate speaker alignment called transient perfect sounds too thin and that a slightly less accurate alignment sounds more real.

Remember the purpose of reproduction is to evoke the feeling this is real so you can suspend what is obvious - namely this is a Hi Fi system and not live. That requires tricking the brain and quite likely slight deviations from strict accuracy will help that.

Thanks
Bill