Claudius I think there's probably a difference between what is difficult/challenging work, and what is generally understood to be hard work.
It's funny because I'm actually hiring right now. The hard part is the fact that our shit pay scale results in a candidate pool that reflects it almost perfectly. I can point to a dozen people I'd love to give the job to, but they'd never take it. I have no power or authority to change that, though. I wouldn't call it hard work. I'd say it's difficult for me to do much of anything at all. Hilariously, we're in desperate need of this hire, but the likely outcome is a failed search and we keep picking up our own slack until circumstances change.
My suspicion is that its not much different at Arsenal. You make your pitch, to your execs and to the desired player(s), and that's pretty much that. Move on to other projects.