What about the modeling sound in particular fails indistinguishable? My ears aren't trained enough.
On a modeling amp, I have not heard one that doesn’t introduce extra digital artifacts into the tone. It’s like the difference between GCI and IRL.
Another is on the other end of the amplitude spectrum, very quiet playing, where I hear extra digital artifacts introduced.
As the other poster mentioned though, these differences may not come across at all in a metal/pop setting.
But there are always exceptions. As someone that worked as a recording engineer for 7 years, and spent time intentionally training my ears with blind tests, I can tell you that there is a definite aural difference between a real tube guitar amp and a modeling amp. Other recording engineers I assisted could hear it too.