Not, exactly no. With Modelers you have umpteen IR possibilities if you run through an FRFR system. The tone is MASSIVELY different with the exact same "amp" settings depending on which IR you chose. If you want to use a power amp and cab, the sound changes depending on the cab set up and power amp used.
When you use a convention amp, you have one set of Amp controls and one cab to deal with.
Why this matters, is that in a modeller like the Axe Fx III, the cab they pair with the amp in the system is what sounds best to the developers as well as the mic position on that Cab IR. That might sound like garbage to you or the rig you are putting it through. Many variables in there which are simply not present when using a conventional Amp/Cab set up.
So it's not "tough luck". It's "how much time do you want to invest to find that sound". My belief is, especially with the Axe Fx II I had, was that it could recreate any sound ever recorded with a guitar. You just have to be willing to invest the time and have the patience to find it.