First of all, I'm a Flickr Pro subscriber, so I'm intimately familiar with all of its features.
In re tagging:
Yes, Flickr has something called "tagging," but it's a different definition of the word "tag." It's a textual field for each photo so that you can assign to it some keywords to make your image more "searchable" for Flickr's built-in search engine. It doesn't actually link the photo to a person's Facebook/Flickr user account.
In re Facebook integration:
Flickr's idea of "Facebook integration" is allowing you to log in to their website with your Flickr credentials (a process that you can expedite by using your Facebook credentials, but you're still having to create a Flickr account) and subsequently letting you post a link on your own Facebook wall to a photo or an album with a tiny thumbnail. Potential viewers then have to navigate away from Facebook into Flickr to view the actual photo(s). And that's if I leave my album wide open to the entire world with no concept of privacy. (which I don't like to do since there are other people in my photos - it's a violation of their privacy) So then if I want to restrict who can see the album, (e.g. my Facebook friends), I have to instruct them to create a Flickr account and then I would have to manually whitelist each of those people. Contrastingly, with the "Facebook photos" system, my "friends" automatically have access and everyone else is blacklisted.
In re "logging in":
Not everyone likes linking their Facebook account with arbitrary websites - especially not when all they want to do is view/comment [on] a photo. And even when someone does link their account, they can still only access private photos after I go in an manually whitelist them. Facebook's built-in photo system lets you view and comment on photos without having to reauthenticate and it lets you do it in situ. In addition to that, it has built-in privacy controls that let you control which groups of people can see which photos.
All things considered, yes, I could put my photos on Flickr and inconvenience my friends/family and potentially violate their privacy, but the cons simply outweigh the pros. And no, I'm not an AOL user (metaphorical or otherwise)... I'm a CS major who doesn't have a lot of free time to manage a hundred different applications strung together by shoestrings and instead prefer to use systems that are robust and integrated.
Also, if you prefer empirical evidence, there was a time when I posted all of my photos straight to a Gallery2 installation on my web server and would post a link to it on my Facebook page. (essentially the same solution as you're proposing) I ended up switching back to the built-in Facebook gallery because comments and views were virtually non-existent. It's very inconvenient to have to leave Facebook to casually view some photos. In case you're unfamiliar with Facebook, photos that are either new or have had lots of recent activity show up in your friends' news feeds. So when they log in, they will see something of this nature: "[friend a] and [friend b] commented on [friend c]'s photo," along with the actual photo. It also shows some of the comments and lets other people join the conversation. That level of interaction isn't present when you just post a link to an external website. My guess is that you've never used Facebook and thus have no knowledge of the distinction, but it's definitely there and it was very apparent to me from my Gallery2 migration experiment.