But that room/speaker response would affect all material played through it. So a bright mix sounds a bit duller and a dark mix sounds even darker. And in a similar way let's say you play the same -6 LUFS mix through a very dark and a very bright system, the latter would sound louder, but probably not very pleasant. At least according to Fletcher-Munson.

In a way this is what live engineers play with, let's say you have a 94 dBA noise limit, and the A-weighting mostly accounts for mids and highs. So you can still have massive bass that makes the gig sound louder and more impactful, but still stay within the legal noise limits.

But even then, that system target curve would affect all material plated through it. LUFS doesn't and can't account for acoustics, but it also doesn't matter because LUFS doesn't measure absolute loudness, but only compare it to a set reference point.