There's also another element: if you have, say, a vintage Fender Champ and a Klon (or whatever) it's because you mean to project different expressions through your string handling and note-playing. At that level you've made a best effort to produce the most emotionally transparent and responsive signal chain, which you will then not think about once you've got it turned on and tweaked: ALL the settings are liable to sound 'good' and respond for you.
The modeling approach is so often "This is exactly that, but better, because here are twelve other Fender Champs and models of Klon to choose from!" and when the first claim isn't as true as we would like, and the second is a distraction and time-sink, that's not great.
I can tell when I've chosen wrongly in my music-making tools, because I flat-out stop making music. Even in a dilettantish way: it just stops being a thing. That's a concern.