Isn't this completely not worthwhile? It'd be cheaper to sell the Rostygold and buy a Tincture of Vigour.

Rostygold sells for 1p, so 100 Rostygold is enough to buy one Tincture; and the Tincture will give -6 CP over 2 actions, while hiring a physician gives -2 CP over 2 actions. Even if you're a Person of Some Importance, it's -2 CP for 1 action, rather than -2 CP for 2 actions.