Then what? I'm guessing the two separate amps would be EQ'd differently. And the point I'm leading to, in addressing the question of potential drawbacks, is that let's say you're playing a repeating major pentatonic pattern, 1-2-3-5-6-5-3-5 for instance, in E starting on the seventh fret on the A string. So you have E and F# on the A string, G# and B on the D string, and C# on the G string. If your A string is EQ'd differently than your D and G strings, then in this example the first two notes of the pattern will sound different than the rest of the pattern. And being a repeated pattern, than difference will be repeated.
I'm just thinking out loud in response to the question. I suppose it depends on how the two amps are EQ'd as to whether the difference on notes played in a pattern that crosses over the threshold moving from the A string to the D string will be significant or not.