What are the best loudspeakers under $4000 to re-create lifelike piano

As always, whart's comments are right on. As for recordings of piano's, direct-to-disk LP's really capture the attack and decay of that instrument like no tape recording I've ever heard. A good piano recording contains an almost instantaneous huge wavefront that instrument creates when struck hard, and reveals the timbre of the instrument changing as it fades away, between notes. The different timbre of specific pianos is a product of the varying levels of the harmonic overtones of the root note---the fundamental. The change in timbre varies amongst different pianos, the relative strengths of fundamental and overtones being unique to each.

IMO, to reproduce the timbre of an instrument with as wide a frequency spectrum as a piano, the loudspeaker itself requires it to have an exceptionally-even octave-to-octave balance. There is no better way to achieve that than to use one driver to reproduce as much of the piano's frequency range as possible, not chop up the keyboard amongst multiple drivers. Achieving even octave-to-octave timbre accuracy via multiple drivers and x/o filters is a very tricky, difficult thing to do. Lifelike timbral reproduction is one reason the original Quad ESL is still as highly regarded as it is. That speaker's ability in that regard remains superior to all but a small handful of competing products, regardless of price!