I hadn't checked it out recently, but it looks like they're still doing fine as far as having a ton of great photos posted. As long as the "community" aspects don't bug you, maybe it's a winning strategy?
OTOH I have no idea if they're profitable or not.
It's fashionable to bash on flickr because it's "languished" and, one redesign aside, hasn't moved a whole lot in a long time. I've certainly taken casual swipes at them myself.
However, the truth is that--while I can imagine some features I'd like--it works pretty well and has a lot of great photography. At the end of the day, it's entirely possible that I wouldn't like it if they were constantly taking the site in new directions because social or mobile or big data or whatever the current hype is.
I haven't been putting any of my photography online for a couple of years now (aside from sharing to friends on Facebook), but the thought had cross my mind recently. It's a tossup between hosting them on my own site or going somewhere else where it can be "social" and more importantly, more broadly visible.
It's not a big thing but the very modest price, the low friction, and contributing to the commons in however small a way work for me.
Flickr decided for a long time to not prioritize the best photo display possible and limited photo size and wouldn't offer things like black backgrounds.
And now I may get an infinite less number views, I don't have to deal with the comments, and photography is no longer associated with gamification (when do I post this for the most views to hit explore, etc).
Flickr has a bit of a "look" to what is popular, and while I'm big on good photo processing and the history of the dark room, what makes it today is often too processed, too HDR, and so on, and playing the "game" is not something I'm interested in.
In the early days of Flickr, people DID look more at all the photos in groups they posted to, and that was pretty great.
Getting more people into photography is great though - just shouldn't be about numbers.