I wouldn't recommend monitoring through a DAW if at all possible.
First is the latency. Even with a powerful computer, getting the buffer size small enough to be usable can be a challenge if you've got a lot of plugins in use in your project. Even under the best of circumstances though, the latency will be noticeable compared to monitoring direct through an analog mixer. One of the most important features of the Axe-FX is the low latency. It would be a shame to lose that key feature by monitoring through a DAW.
Second is the issue of audio quality. Even modest analog mixers like the ones described in the recording guide have excellent audio quality. Remember, this is just for monitoring. The record signal path does not go through the mixer.
Third is convenience. Monitoring through a DAW would mean turning on the computer, launching your DAW and loading a project suitable for monitoring purposes. That can be a factor in those moments when you want to quickly pick up your guitar and play immediately when inspiration hits.
That's not to say there aren't times where it is appropriate to monitor through a DAW. For example, if you have plugin that you want in your monitoring signal path, then you should monitor through your DAW. That's why there's a section in the recording guide to cover that scenario. But otherwise, there's really no reason to monitor through a DAW. A good mixer for this purpose costs less than $60, so you're not going to save much money by not using a mixer.
P.S. If you look at configurations #3 and #5 in the recording guide, note the mixer and interface are mutually exclusive. You would use one or the other. In other words, if you already have an interface, you can use #5 and there's no need for a mixer.
