I think the question is biased. Consider it the other way around: is functional programming becoming OOP?
Let's make a small thought experiment. Let's consider a classical MVC architecture. The values are in the model, the functions that work on those values are in the controller, the view provides interactivity with the users, based on their actions (events) it calls the controller to operate on the model, either modify it, display some (possibly modified) values from it, or both.
If we implement the controller with something purely functional there are not going to be any mutable values in it whatsoever. All the values, mutable or not, are going to be in the model.
Now let's group those functions together into objects, and call them methods, and let's put some configuration values (like the database username and password) inside those objects (let's call them attributes), and let's keep those values as completely immutable. Anyway we didn't really need to add those values, they probably were constants in our functional source code, but it's still nice to have them as immutable attributes.
What you say is that now those objects in the controller, are no longer transformations (functions) on the data but values that "can't do any work, work is done on them", simply because we added some attributes and we made those values immutable. I think that's not fair and I think the question isn't well defined.
Also I think that as software grows larger it's normal to see big chunks of code (methods, files, modules, or even libraries) that only do some of the things software can do, either storing values, transforming them, displaying them, etc. This isn't necessarily a bad thing, if that allows (or that is needed for) building bigger and better software then I'd say it's a good thing.