I think that to most people where having a waifu actually means a lot, they are filling for something currently missing in their lives. Well that's the impression I got from listening to this podcast by HealthyGamerGG:
To be quite frank, I never had an experience like how the person describes in the video (I guess that's a good thing?)
Instead, it seems that my "waifu", in this case Patchouli would end up serving more of what I chose (and didn't choose) as part of my online "branding" so to speak, and having her represent me in the internet leads to more familiriaty, in turn making me like the character more simply because I've gotten so used to them. So yeah, I can't really explain why patchouli is my "waifu". Are they my waifu? I don't really imagine a married life iwth "patchouli knowledge" either. XD
But upon further introspection, it is true that there's some characteristics about her that I admire. So in a way, those aspects of serving as " comfort character" or even just as a form of motivating myself to reach my goals plays a role here. Patchouli is wise, cool and thoughtful, she also seems to know a lot of things, and those are all qualities I want to have for myself. The complexities of human relationship with others don't seem to be lost even when talking about fictional characters, it seems. :P
As for your comments about what seem to be (mostly) gacha characters, I believe they are fundamentally different from touhou, in the sense that these are made from concept to be marketable (to men, for the most part), even if, ultimately, they are both examples of idealized concepts of people (and as we know, fantasy trumps reality in the eyes of the one that becomes enamoured by it), the point is that these character shoot for combinations that make them attractive to the fans upon tried and true industry tradition, similar to how the idol industry works. I believe it's good to be critical of waht makes these characters "waifus" for you, as they are often superficial traits that just appeal to your specific yearnings of one nature or another.
(Not to be a killjoy however, it's good to find things you enjoy regardless). Also, on unrelated note: Your tastes seem very similar to another friend of mine judging by the examples you provided alone :p
To conclude: At first glance, I guess it would be easy to equate a waifu to a non-existant wife, but the point of all my ramblings is that these relantioships are more complex and of a different nature, In my opinion. For you to genuinely attempt to replace a real human with a 2d companion, you'd have to be unique circumstance not common even among us weebs. In this, I find the comments made in question 3 of the FAQ you sent to be exceptionally pertinent here.
Also, I've been wanting to watch azumangah daioh. It seems to be similar to the likes of nichijou (both "My Ordinary Life" and "Danshi Koukousei", which I enjoyed a great lot) maybe I'll finally take the time to give it a watch and join the discussion.
Thanks for reading my ramblings, I hope it made sense. Cana out. :P