Fat models are slightly better than having that crud in your views, but they're still an antipattern. Models should describe the relationships between entities in your business, not be the junk drawer for stuff that doesn't go anywhere else. Fat models are already a code smell, but passing the request object to your model should really set off alarm bells. You've now made it extremely messy to use your models outside…
I really want to know where to put that stuff. Creating an object to put the "filterBlah" function that you only use once is overkill, so it sits there as a one-off method in your View or Controller or Model. I've worked with large enough code bases for long enough that I know there's always hacky junk there, and I'd just like to know more strategies for addressing it. Do large code bases have a strategy for putting the one-offs in a place where they are obvious and organizable?
I'm now working on a 5M line code base, and at that scale, you kind of have to put the code into acceptable, bad, worse and awful categories and come up with strategies to fix it. There IS no good code at this point. I've actually done refactoring with regexes, but I want better tools for reasoning about extremely large and weird code bases.