On the web, the user is rarely a monolith. For a lot of websites (as compared to, say, business software or automobiles), the user could be everyone and anyone. They may all have different mental models, expectations, abilities, etc.
This is important to keep in mind when focusing on user centered design for a general purpose website. You need a testing pool representative of your users (or who you want your user to be), you need to figure out what to do if there are conflicts among users, during testing, etc. It might be obvious, and you can probably still fit in into a framework, but what I'm getting at is that it is less empirical than it might seem at first pass. There is still an art to user centered design, and if you have this in mind, your designs don't have to look hopelessly outdated.
> On the web, the user is rarely a monolith.
Usability folks have understood this for decades. Alan Cooper was writing about defining multiple separate personas [1] to represent different cohorts of your userbase in the 90s.
> what I'm getting at is that it is less empirical than it might seem at first pass.
I would argue that it is still exactly as empirical. You just have to be careful how you aggregate your data and don't try to reduce things to too few clusters. Otherwise you end up making the classic mistake of offering a single T-shirt size at your conference that mostly only fits men because they are the majority of attendees.
> There is still an art to user centered design,
Agreed. No amount of analysis will do your synthesis for you. You still have to make.
[1]: https://en.wikipedia.org/wiki/Persona_(user_experience)