Is it live or is it?

I, too, listen to unamplified acoustic music but the mystery can be resolved. The horm-loaded systems are part of the music production/creation chain and their characteristics are included in the recording you buy. The home system should not have any characteristics, in the ideal, because they are part of a music reproduction/recreation chain.

Kr4 is right on that one. A lot of people make that mistake. The application is different,and you need to use the right tool for the right job.

The only thing I would add is that the OP's statement is usually not correct. Just because you're in the audience listening to the concert through a PA system, doesn't mean they're setting up mics and recording the PA system. Recording engineers usually tap into the signal at some point, such as the mixing board, before it goes to the PA. So what they're recording is not the same as what you here as a member of the audience.

Try small amps and big horns at home.
And try not to scrimp. :)

If your home listening space were the size and shape of a concert hall venue, then you would probably use a horn based speaker array at home. If your home listening space is that of a typical domestic room, then there are more suitable choices. And yes, there is a difference between music production and music reproduction.

Why would one pay large amounts of money to go 'hear' loud amplified music at concerts? Certainly not for the 'hearing'. It is all about begin there, nothing else. Do I go to live concerts? Yes, but only ones' that are in small settings where there is no amplification, these are mostly small jazz clubs. A perfect example of one such site in the Dizzy Club in Lincoln Center. You hear real live music.