Agreed! Why should they have done that? There was the implication of financial reasons, but seven years with House (I count the one spent playing Diagnostics' personal surgeon) should have taught Chase enough to keep things going. In terms of PR, finances, whatever standard you want to measure by, it would have been better than shutting the department down altogether. (Cuddy kept it open for Foreman when House was ostensibly quitting; why shouldn't Chase have been given a chance this time?)

And anyway, textually, canon has established that Chase is the go-to for creative angles when House is indisposed; the writers should have taken that and run with it.