That's a bit of a false equivalence.
The FA Cup is regarded far more highly than any other domestic cup.
With the rise of the CL it has somewhat lost its sheen admittedly but I still regard it fairly highly and it's still a "thing" in the way the league cup really isn't.
Don't get me wrong, I don't think it would be enough given the spend Arteta has been allowed. But it's not nothing.