If we assume that the respective colorations are essential to getting the sound "right," then I would say it couldn't happen, at least not without applying EQ. OTOH, rock music played through classic ARs has always sounded just fine to me (if I have visitors with "west coast" preferences, I tell them to just wait until I'm out of the room and then press that button marked "Loudness"), while classical music played through "west coast" speakers usually makes me want to reach for the bass and treble controls (to turn both down). So from my totally subjective POV, the speakers I have do in fact play both "with equal aplomb." Ultimately, it seems to me that "east coast" and "west coast" reflect the subjective preferences of listeners (myself included) rather than any objective requirement of a music genre.
Soundminded observes that, in detail, the parameters must be adjusted for virtually every cut. He's not the first to suggest this.
On the larger scale, however, there's a conspicuously large gap between what are considered rock (L100) vs. classical (AR3a) speakers. Call it west vs. east coast perhaps, but each may be characterized by their respective coloration.
Is it inconceivable that an ideal loudspeaker could play either or both with equal aplomb?
I would be inclined to agree with the "EQ every record" philosophy if objective data about what settings are required for every record came with it. In the absence of this, EQ'ing is still just an exercise in tailoring sound to a listener's subjective view of what sound is "right," and while I might eventually be able to do that for a Rubenstein recording made in a symphony hall I"m familiar with, when it comes to adjusting for Pink Floyd in any venue I'd be utterly lost.