Perhaps I don't know enough about the actual profiling process, but thinking logically, surely the amps tone would have been set to get the best out of the guitar being used?....so a strat would be EQ'd differently than a Les Paul, and in that case, once profiled for a strat, if you used an LP, you'd struggle to get near the demo sounds?
That's not always the case. some guys set the amp up at a neutral dialed at noon state to allow the user to mod the EQ on the Kemper. They even try to use a more or less "neutral" speaker. I always offer many different EQ settings so you can ideally find one that works for you.