I think it's more like, out of this actual, physical cow, we are going to carve a perfectly spherical cow plus some... "other" parts.

That is, you can make chunks of your application functional - they just can't be chunks that touch the exterior. It's not a "mental model" - it's something you construct in the code.

Now, you may not be able to do that with all the "interior" code, either. Parts may have too much intrinsic state for functional programming to be a useful approach. But for other interior parts, hey, you like functional? Make it so.