Square- NO! As total volume goes up, amplifier power to reach a specific sound pressure level goes up. 16' ceiling will be more than 2x the volume of a conventional room w 7.5' ceilings.
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I think your large room presents challenges but if you meet them, it should work very well.
Among the challenges are these:
1) Assuming your listening distances will be greater than in a normal room, the reverberant field will be stronger relative to the first-arrival sound. Since the reverberant field will be making a greater contribution to percievel timbre, you want speakers that do a good job in that area. If not, the timbre of voices and instruments will not be natural-sounding.
2) Your speakers will have to work considerably harder to reach a given loudness level in a room that big, so you want a speaker/amplifier combination that can get there without either becoming strained. Rated power handling alone doesn't tell the whole story; for instance, most woofers run into excursion limitations well before they reach their thermal limits.
3) A big room like that provides less reinforcement in the bass region than most speakers are typically "voiced" for, so most speakers will sound anemic in a room that large.
On the other hand, a large room results in long-length-induced delays before the onset of reflections. This is highly desirable from a psychoacoustics standpoint, and if this relatively late-arriving reverberant field is dominated by lateral reflectsions (that is, reflections off the side walls) the sense of "envelopment" or "immersion in the acoustic space" can be pretty spectacular. So if you can put together a system that addresses the challenges, the potential rewards are quite good.