Yours is a valid question, as there are always going to be things not in the Axe Axe Fx III line. This is true of amp and cab blocks, as well the number of scenes/channels/controllers available that might be a limitation for some but are a limitless ocean to most. The better question for every player is “What do I need/use that it doesn’t do?” Some here have listed theirs, and each is true for the player who needs it. I encourage you to delve into the plethora of effects it can do, as it’s astounding, and not get too caught up in the one it won’t. Should you eventually need something that can’t be done, grab a “real” version of what you’re missing and stick it in line with your Axe Fx. You really can “have it all your way” with that approach.
I’m not taking your question as negative, by the way. It’s a good thing to know if you’re a heavy esoteric effects user considering an Axe Axe Fx III purchase. I’m just encouraging you towards making the music you make and not worrying over shortcomings you may never notice.
