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.
You know...that's fair enough.
And I did that for a long time. It's not an option for me now if I want to use my good speakers, and maybe I just got used to it. But, to explain my position...
I literally always have a Reaper session running. None of my audio gets to my main speakers without it. Because it's doing an active multi-way thing. All the crossovers and routing happen in that reaper session, which is essentially a monitor controller. System audio goes through S/PDIF (because Windows is stupid and won't send system audio through ASIO), and the audio applications I actually use go through ReaRoute (or I import the track group that does the routing/XOs to a reaper project if I'm working in Reaper). I have a version of it that's all linear-phase filters for super-accurate playback and one with all zero latency filters for low-latency monitoring. The FM3 inputs (and a few others) are only in the low-latency version of my standard monitor controller session. And the linear-phase version runs higher buffers because the linear phase filters incur about a second of latency anyway. So, at that point, it doesn't matter. And I just don't use that for anything that requires live monitoring.
The PC is an i7 8086k with the 5GHz boost clock set to affect all cores, a bunch of ram, all NVMe and 10GbE storage, and it was "tweaked" to not run a lot of the windows bloat (cortana, telemetry, xbox, windows store....all gone) and for prioritizing background processes (which include audio for some reason). I certainly can't game on it like this, but I don't do that anyway. And I can run a 32-sample buffer at 44.1 or 48k easily. I don't actually lose timing until I get over 128 samples @ 44.1 or 48. So, there's some room left if I need it.
Despite all the plugins that I normally have running (14-28, depending on what I'm doing), the zero latency version shows 0 samples of latency session-wide for processing with about 2-5% CPU usage as standard (web browsers take more resources, because modern web is all bloat). The IO buffers account for under 1.5ms total latency. There's a bit more than that in real life because of how long my converters take to actually do things, but it's still under 4ms round-trip, no DPC latency spikes, and no dropouts.
Reaper is a big part of it. It's just plain more efficient with computer resources than every other DAW. I've done this kind of setup before using Ableton Live and Pro Tools, and they couldn't really handle this kind of a setup without a bigger buffer. Switching to Reaper made a bigger difference in "feel"/capabilities of the DAW than the first time I tried UAD cards or the first time I used Pro Tools HD. The difference is not subtle, though obviously YMMV.
If you use a digital mixer at any point (which you do if you play live...I haven't seen an analog FOH or monitor console in at least a decade), you can set up something similar at home, and you probably already have the hardware you need to do it. This kind of a setup will work with a relatively cheap Focusrite audio interface. You can do even better with Thunderbolt or PCIe. And even with as good as it is, Reaper is $60 unless you make enough money from music to buy the more expensive license and are honest about it.
Maybe your setup/needs are different. If you're running a bunch of heavy plugins for synths, drum machines, etc. on the same computer, I could see that causing problems. But if you're doing that, it's not hard-in any DAW-to freeze tracks while you're recording or print to audio as you need to while you need low-latency monitoring. If your setup is very "big" and you want the flexibility of waiting a long time to print to audio, there are a lot of ways to offload that processing that can wind up "better" than running through a budget mixer and then-essentially-having to do a monitor mix separate from your rough.
It's all different strokes, in the end. But, unless the setup causes you problems....don't discount just monitoring through a DAW. Low-latency monitoring isn't nearly as hard as it was just a few years ago. And a few milliseconds really isn't a big deal. It's one of those things that will bother you only if you obsess over it.