There are many advantages. Less maintenance, lower stage volumes, better for in-ear-monitoring use, sound consistency, less weight to carry, and the ability to explore hundred of amps sounds with a single device eg. check https://wiki.fractalaudio.com/wiki/index.php?title=Amplifier...
I would be pretty surprised if Metallica were using the technology you are describing. They have an extremely consistent setup that has worked for decades and an effectively infinite budget.
That’s just one concrete example.
I think a lot of the comments in this thread are missing the fact that if a player thinks a thing has irreproducable properties, they may be happier and more creative while using it.
https://www.youtube.com/watch?v=P6k2ghtbhoU 3:09-7:32.
Megadeth is also using AxeFX. https://www.youtube.com/watch?v=O7vzOjzn0Mw
And from there you can extrapolate how common they are.