Mustafar is a mining colony on the Outer Rim and Coruscant is the heart of the galaxy. Could the emperor not find a DD-13 medical assistant and 2-1B surgical droids anywhere else closer to Mustafar? Could Kamino clone tech be on Coruscant?
The very prominent reason might be because the Emperor knew that Anakin would last the time back to Coruscant (they literally jumped to lightspeed), also because Coruscant was the capital of the galaxy and the Emperor wanted his new apprentice to receive the best quality of medical attention. Since the galaxy was now under the control of the Sith overlords, he wanted to ensure that every planet in the galaxy knew about their power and influence. There were no Jedi warriors left to fight or resist them.