In the old days, the main reason to use your effects in parallel with your dry signal was to ensure the integrity of your dry signal. There were other reasons too, depending on what type of effect you were after, but the big one IMO was the audio quality of the dry signal.
Most digital effects (Eg. Yamaha SP-90) back then had analog dry signal paths that were not of the highest quality.
If you ran your preamp into the effect then you would normally mix the wet/dry balance within the effect's mixer which would degrade the quality of your dry signal somewhat.
If you ran that effect into another effect in series then you would be doubling the problem. The cables used to connect things would also degrade the signal.
Etc.
By using a parallel path for the dry signal, via a high quality line mixer, you could keep the dry signal as pristine as possible.
If you used two effects in parallel, rather than in series, you could do things like not having your chorused signal go through your reverbs or delays, etc.
But I generally like to have my chorused signal go through my echos and reverbs, so that parallel routing is generally not for me. I prefer things in series most of the time, for the sound.
At some point the manufacturers began digitizing the dry signal too, first at 16 bits then at 24 bits.
In my opinion, because this was generally a bit less noisy than an analog dry path and had a fuller frequency response, many of us didn't notice the more subtle ways that the dry signal was being degraded by things like a harsh tone at both ends of the audible frequency spectrum and the introduction of noticeable latency. But because everything inside the effects was in the digital domain it made less sense to do parallel routing within the effect for the purpose of maintaining the best sounding dry signal. Still, if you were like me and you noticed the degradation of the dry signal by virtue of it being digitized, it was worth it to carry a line mixer around with you and mix the dry signal in parallel thus keeping it in the analog domain the entire time.
The Axe, actually fits the mold of the above description. It digitizes the dry signal at 24 bits 48khz.
But the Axe's digital converters are superior to anything else on the market and Cliff has also designed an electronic front end to the Axe that maintains your signal all the way the through even though it's being sampled. IMO It's a first in the digital guitar effects world. Latency is nearly non-existent and is not normally even noticeable, even when you're looking for it. Plus, any cabling that connects one Effects Block to another is virtual and perfect in that it will not degrade the signal at all. It's really the ideal signal path.
So, IMO, there is less reason than ever to use a parallel effects routing when using the Axe if all you're trying to do is maintain the integrity of your dry signal. The Axe maintains the integrity of your dry signal anyway.
On the other hand, if you really want the sonic effects of what parallel routing can do for you, it's all possible with the Axe, in spades. And there are all sorts of interesting sounds that can only be achieved by putting things in parallel.
Just my 2c.