I think I've seen these phones in use at a local hospital, and it does seem like a good idea.

However, any time an employer says "a shortage of <employee-type X>, I ask myself "how long would it take to fill that shortage if they offered ten times as much money?" How many former nurses would come out of retirement, or would switch their career back to nursing, and how long would it take to train a whole lot of new nurses, if hospitals started offering to pay doctor's salaries to their nurses?

I'm not saying that's really possible, just that it's something to think about.

Think of it as the flip side of the conservative argument that minimum wage laws cause unemployment, on the grounds that if employers could pay less, they could afford to hire more people. The converse is that if employers offered more money, they'd attract more candidates.